Changeset 315439 in git
- Timestamp:
- Feb 14, 2018, 11:20:48 AM (6 years ago)
- Branches:
- (u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')
- Children:
- 46d2096280c2de450bd4e185b966383a4bed594d
- Parents:
- 0e896f8ca74d72438d1a89b85be8d786a1bf3f3c
- Files:
-
- 2 edited
-
doc/singular.idx (modified) (76 diffs)
-
emacs/hlp-cmpl.el (modified) (30 diffs)
Legend:
- Unmodified
- Added
- Removed
-
doc/singular.idx
r0e896f r315439 169 169 ? sing_36.htm#IDX106 170 170 ? sing_259.htm#IDX148 171 ADGT sing_945.htm#SEC1021 65350 171 172 AG codes sing_854.htm#SEC906 172 AGcode_L sing_1 798.htm#SEC187460329173 AGcode_Omega sing_1 799.htm#SEC187556285173 AGcode_L sing_1800.htm#SEC1876 60329 174 AGcode_Omega sing_1801.htm#SEC1877 56285 174 175 ASCII sing_904.htm#SEC980 26816 175 176 ASCII links sing_117.htm#SEC157 176 177 ASSUME sing_64.htm#SEC101 177 A_L sing_149 7.htm#SEC157316721178 A_L sing_1499.htm#SEC1575 16721 178 179 A_Z sing_903.htm#SEC979 50866 179 180 Access to elements of a user defined type Access to elements of a user defined type sing_185.htm#SEC225 180 Adj_div sing_179 3.htm#SEC186944919181 Adjoint ideal sing_137 4.htm#IDX618182 Alexander polynomial sing_14 68.htm#IDX642183 Algebraic Geometry codes sing_179 2.htm#IDX790181 Adj_div sing_1795.htm#SEC1871 44919 182 Adjoint ideal sing_1376.htm#IDX611 183 Alexander polynomial sing_1470.htm#IDX635 184 Algebraic Geometry codes sing_1794.htm#IDX783 184 185 Algebraic dependence Algebraic dependence sing_833.htm#SEC885 185 Algebraic geometry sing_13 49.htm#SEC1425186 Algebraic geometry sing_1351.htm#SEC1427 186 187 AltVarEnd sing_746.htm#SEC798 11020 187 188 AltVarStart sing_745.htm#SEC797 21592 188 Ann sing_12 88.htm#SEC136461560189 Ann sing_1290.htm#SEC1366 61560 189 190 Appel function sing_563.htm#IDX351 190 191 Appel hypergeometric function sing_563.htm#IDX352 191 192 Applications sing_852.htm#SEC904 192 Arnold, classification. sing_232 0.htm#IDX946193 Arnold, classification. sing_232 1.htm#IDX947194 ArnoldAction sing_159 0.htm#SEC166626958193 Arnold, classification. sing_2322.htm#IDX939 194 Arnold, classification. sing_2323.htm#IDX940 195 ArnoldAction sing_1592.htm#SEC1668 26958 195 196 Assignments for user defined types Assignments for user defined types sing_187.htm#SEC227 196 197 AssocTanToEnv sing_940.htm#SEC1016 46214 197 Atkin sing_188 1.htm#SEC1957sprintf198 Atkin sing_1883.htm#SEC1959 sprintf 198 199 Authors sing_1.htm#IDX16 199 Automatic Deduction of Geometric Theorems sing_923.htm#IDX426 200 BINresol sing_1387.htm#SEC1463 52996 200 Automatic Deduction sing_945.htm#IDX482 201 Automatic Demonstration sing_945.htm#IDX483 202 BINresol sing_1389.htm#SEC1465 52996 201 203 Background sing_3.htm#SEC5 202 204 Basic programming sing_808.htm#SEC860 203 205 Basic programming sing_808.htm#SEC860 204 BelongSemig sing_231 6.htm#SEC239222405205 BerlekampMassey sing_237 1.htm#SEC24472172206 Bern sing_22 89.htm#SEC236564051206 BelongSemig sing_2318.htm#SEC2394 22405 207 BerlekampMassey sing_2377.htm#SEC2453 2172 208 Bern sing_2291.htm#SEC2367 64051 207 209 Bernstein operator sing_540.htm#IDX333 208 210 Bernstein-Sato polynomial sing_505.htm#IDX314 209 211 Bernstein-Sato polynomial sing_540.htm#IDX330 210 Bernstein-Sato polynomial sing_153 1.htm#IDX673211 Bernstein-Sato polynomial sing_153 5.htm#IDX690212 Bernstein-Sato polynomial sing_1533.htm#IDX666 213 Bernstein-Sato polynomial sing_1537.htm#IDX683 212 214 Bernstein-Sato polynomial for variety sing_596.htm#IDX355 213 Betti sing_250 0.htm#SEC257621134215 Betti sing_2507.htm#SEC2583 21134 214 216 Betti number Syzygies and resolutions sing_870.htm#SEC927 215 BettiNumsH sing_240 1.htm#SEC247718661216 BettiNumsN sing_24 06.htm#SEC248244681217 BettiNumsS sing_24 04.htm#SEC248014964217 BettiNumsH sing_2407.htm#SEC2483 18661 218 BettiNumsN sing_2412.htm#SEC2488 44681 219 BettiNumsS sing_2410.htm#SEC2486 14964 218 220 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_880.htm#SEC937 219 BlowingUp sing_151 0.htm#SEC158643153220 Blowupcenter sing_139 0.htm#SEC14663423221 BorelCheck sing_146 5.htm#SEC154148787222 Bott's formula sing_2 695.htm#IDX1047221 BlowingUp sing_1512.htm#SEC1588 43153 222 Blowupcenter sing_1392.htm#SEC1468 3423 223 BorelCheck sing_1467.htm#SEC1543 48787 224 Bott's formula sing_2702.htm#IDX1045 223 225 Branches of space curve singularities Branches of space curve singularities sing_841.htm#SEC893 224 226 Briancon-Maisonobe algorithm sing_540.htm#IDX339 225 Brieskorn lattice sing_153 1.htm#IDX669226 Brieskorn lattice sing_153 2.htm#IDX680227 Brieskorn lattice sing_153 3.htm#IDX683228 Brieskorn lattice sing_153 4.htm#IDX686229 Brieskorn lattice sing_153 5.htm#IDX689230 Brieskorn lattice sing_153 6.htm#IDX693231 Brieskorn lattice sing_153 7.htm#IDX697232 Brieskorn lattice sing_15 38.htm#IDX703233 Brieskorn lattice sing_15 39.htm#IDX711234 Brieskorn lattice sing_154 0.htm#IDX717235 Brieskorn lattice sing_154 1.htm#IDX725236 Brieskorn lattice sing_154 2.htm#IDX735237 Brieskorn lattice sing_155 3.htm#IDX741238 Brieskorn lattice sing_155 5.htm#IDX752239 Brieskorn lattice sing_158 3.htm#IDX779240 Brill-Noether algorithm sing_179 2.htm#IDX791241 BrillNoether sing_179 5.htm#SEC187139919227 Brieskorn lattice sing_1533.htm#IDX662 228 Brieskorn lattice sing_1534.htm#IDX673 229 Brieskorn lattice sing_1535.htm#IDX676 230 Brieskorn lattice sing_1536.htm#IDX679 231 Brieskorn lattice sing_1537.htm#IDX682 232 Brieskorn lattice sing_1538.htm#IDX686 233 Brieskorn lattice sing_1539.htm#IDX690 234 Brieskorn lattice sing_1540.htm#IDX696 235 Brieskorn lattice sing_1541.htm#IDX704 236 Brieskorn lattice sing_1542.htm#IDX710 237 Brieskorn lattice sing_1543.htm#IDX718 238 Brieskorn lattice sing_1544.htm#IDX728 239 Brieskorn lattice sing_1555.htm#IDX734 240 Brieskorn lattice sing_1557.htm#IDX745 241 Brieskorn lattice sing_1585.htm#IDX772 242 Brill-Noether algorithm sing_1794.htm#IDX784 243 BrillNoether sing_1797.htm#SEC1873 39919 242 244 Buchberger algorithm for toric ideals Buchberger algorithm sing_881.htm#SEC938 243 245 Budur-Mustata-Saito approach sing_596.htm#IDX359 244 Building Singular sing_275 2.htm#SEC2841246 Building Singular sing_2759.htm#SEC2848 245 247 C programming language Major differences to the C programming language sing_409.htm#SEC449 246 248 C, module ordering sing_862.htm#IDX413 247 CGS sing_925.htm#IDX4 35248 CM_regularity sing_145 2.htm#SEC152833865249 CMtype sing_162 1.htm#SEC169724849249 CGS sing_925.htm#IDX426 250 CM_regularity sing_1454.htm#SEC1530 33865 251 CMtype sing_1623.htm#SEC1699 24849 250 252 CRHT-ideal sing_887.htm#SEC951 251 CSMA sing_231 2.htm#SEC238849080253 CSMA sing_2314.htm#SEC2390 49080 252 254 CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33 253 Canonical Forms sing_923.htm#IDX424 254 Castelnuovo-Mumford regularity sing_1452.htm#IDX634 255 Castelnuovo-Mumford regularity sing_1454.htm#IDX627 255 256 Category string sing_51.htm#SEC88 256 257 CenCharDec sing_702.htm#SEC754 44505 257 Center sing_14 29.htm#SEC150525541258 CenterBO sing_143 6.htm#SEC151234701258 Center sing_1431.htm#SEC1507 25541 259 CenterBO sing_1438.htm#SEC1514 34701 259 260 CentralQuot sing_700.htm#SEC752 56490 260 261 CentralSaturation sing_701.htm#SEC753 31585 261 262 Change of rings sing_9.htm#SEC15 262 263 Characteristic sets sing_871.htm#SEC928 263 CharacteristicExponents CharacteristicExponents sing_151 6.htm#SEC159221795264 ChernClass sing_27 08.htm#SEC278432965265 ChernRootsDual sing_22 68.htm#SEC234440100266 ChernRootsHom sing_227 7.htm#SEC235348446267 ChernRootsProd sing_227 0.htm#SEC234613967268 ChernRootsSum sing_226 6.htm#SEC234257286269 ChernRootsSymm sing_22 79.htm#SEC235559304270 ChernRootsWedge sing_228 0.htm#SEC23567239271 Chevalley-Rosenlicht theorem sing_13 68.htm#IDX603272 Chevalley-Rosenlicht theorem sing_13 69.htm#IDX606273 Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_2 699.htm#IDX1052274 ChowRing sing_2 699.htm#SEC277557977264 CharacteristicExponents CharacteristicExponents sing_1518.htm#SEC1594 21795 265 ChernClass sing_2715.htm#SEC2791 32965 266 ChernRootsDual sing_2270.htm#SEC2346 40100 267 ChernRootsHom sing_2279.htm#SEC2355 48446 268 ChernRootsProd sing_2272.htm#SEC2348 13967 269 ChernRootsSum sing_2268.htm#SEC2344 57286 270 ChernRootsSymm sing_2281.htm#SEC2357 59304 271 ChernRootsWedge sing_2282.htm#SEC2358 7239 272 Chevalley-Rosenlicht theorem sing_1370.htm#IDX596 273 Chevalley-Rosenlicht theorem sing_1371.htm#IDX599 274 Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_2706.htm#IDX1050 275 ChowRing sing_2706.htm#SEC2782 57977 275 276 Classification of hypersurface singularities Classification of hypersurface singularities sing_842.htm#SEC894 276 Classification of singularities sing_26 68.htm#IDX1023277 Classification of singularities sing_2675.htm#IDX1021 277 278 Code Codes and the decoding problem sing_886.htm#SEC944 278 279 Codes and the decoding problem Codes and the decoding problem sing_886.htm#SEC943 279 Coding theory sing_179 1.htm#SEC1867280 Coefficient rings Notes for Singular users sing_275 0.htm#SEC2834280 Coding theory sing_1793.htm#SEC1869 281 Coefficient rings Notes for Singular users sing_2757.htm#SEC2841 281 282 Command line options Command line options sing_19.htm#SEC26 282 283 Commands Functions and system variables sing_206.htm#SEC246 283 284 Commands for user defined types Commands for user defined types sing_186.htm#SEC226 284 285 Commutative Algebra sing_821.htm#SEC873 285 Commutative algebra sing_110 4.htm#SEC1180286 Commutative algebra sing_1106.htm#SEC1182 286 287 CompDecomp sing_502.htm#SEC554 9959 287 CompInt sing_2318.htm#SEC2394 7518 288 CompleteHomog sing_2256.htm#SEC2332 42123 289 ComplexValue sing_2393.htm#SEC2469 45546 290 Comprehensive Groebner System sing_925.htm#IDX438 291 Comprehensive Groebner Systems sing_923.htm#IDX422 288 CompInt sing_2320.htm#SEC2396 7518 289 CompleteHomog sing_2258.htm#SEC2334 42123 290 ComplexValue sing_2399.htm#SEC2475 45546 291 Comprehensive Groebner System sing_925.htm#IDX429 292 292 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_817.htm#SEC869 293 ConsLevels sing_933.htm#SEC1009 23520 294 ConsLevelsToLevels sing_934.htm#SEC1010 32625 295 Constructible sets sing_923.htm#IDX430 296 ContactMatrix sing_1518.htm#SEC1594 40767 293 ConsLevels sing_933.htm#SEC1009 14282 294 ContactMatrix sing_1520.htm#SEC1596 40767 297 295 Conti-Traverso algorithm sing_876.htm#SEC933 298 296 Contributors sing_1.htm#IDX15 299 297 Control structures sing_377.htm#SEC417 300 Control theory System and Control theory sing_182 5.htm#SEC1901298 Control theory System and Control theory sing_1827.htm#SEC1903 301 299 Cooper philosophy sing_887.htm#SEC949 302 Cornacchia sing_187 1.htm#SEC194763434303 CornacchiaModified sing_187 2.htm#SEC194859790300 Cornacchia sing_1873.htm#SEC1949 63434 301 CornacchiaModified sing_1874.htm#SEC1950 59790 304 302 Crep sing_928.htm#SEC1004 17485 305 303 Critical points sing_836.htm#SEC888 306 CurveParam sing_151 2.htm#SEC158853605307 CurveRes sing_151 1.htm#SEC158748848308 Curves sing_137 4.htm#IDX615304 CurveParam sing_1514.htm#SEC1590 53605 305 CurveRes sing_1513.htm#SEC1589 48848 306 Curves sing_1376.htm#IDX608 309 307 Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36 310 Cyclic code sing_180 6.htm#IDX798308 Cyclic code sing_1808.htm#IDX791 311 309 Cyclic roots sing_814.htm#SEC866 312 310 D-integration sing_563.htm#IDX348 … … 331 329 Decker, Wolfram sing_1.htm#IDX17 332 330 Declaration of objects of a user defined type Declaration of objects of a user defined type sing_184.htm#SEC224 333 Decoding sing_180 6.htm#IDX800331 Decoding sing_1808.htm#IDX793 334 332 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_885.htm#SEC942 335 333 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_890.htm#SEC960 … … 337 335 Deformations sing_839.htm#SEC891 338 336 Deformations, T1 and T2 sing_838.htm#SEC890 339 Deg sing_25 03.htm#SEC257935419340 Degree sing_25 04.htm#SEC258048523341 DegreePure sing_135 3.htm#SEC142933003342 Degrees sing_25 05.htm#SEC258150349343 Delta sing_143 7.htm#SEC151333497344 DeltaList sing_14 38.htm#SEC151465148337 Deg sing_2510.htm#SEC2586 35419 338 Degree sing_2511.htm#SEC2587 48523 339 DegreePure sing_1355.htm#SEC1431 33003 340 Degrees sing_2512.htm#SEC2588 50349 341 Delta sing_1439.htm#SEC1515 33497 342 DeltaList sing_1440.htm#SEC1516 65148 345 343 Demo mode sing_24.htm#SEC35 346 344 Depth sing_828.htm#SEC880 347 Determinacy sing_267 1.htm#IDX1027345 Determinacy sing_2678.htm#IDX1025 348 346 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_879.htm#SEC936 349 Distributed computing sing_95 4.htm#IDX496347 Distributed computing sing_956.htm#IDX489 350 348 Dlocalization sing_781.htm#SEC833 22140 351 349 Documentation Tool sing_60.htm#SEC97 … … 353 351 Ds, local ordering sing_861.htm#IDX406 354 352 DsingularLocus sing_785.htm#SEC837 46495 355 Dynamic Geometry sing_923.htm#IDX427356 353 Dynamic loading sing_71.htm#SEC111 357 354 Dynamic modules sing_816.htm#SEC868 358 ECPP sing_191 5.htm#SEC199155777359 ECoef sing_139 6.htm#SEC147214154360 EOrdlist sing_139 4.htm#SEC147036329355 ECPP sing_1917.htm#SEC1993 55777 356 ECoef sing_1398.htm#SEC1474 14154 357 EOrdlist sing_1396.htm#SEC1472 36329 361 358 ERROR sing_236.htm#SEC276 362 359 ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33 363 Edatalist sing_139 3.htm#SEC146961593364 Edelman-Reiner sing_2 199.htm#IDX881360 Edatalist sing_1395.htm#SEC1471 61593 361 Edelman-Reiner sing_2201.htm#IDX874 365 362 Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37 366 363 Editing input sing_18.htm#SEC25 … … 375 372 Emacs, running Singular under Running SINGULAR under Emacs sing_23.htm#SEC30 376 373 Emacs, user interface Emacs user interface sing_21.htm#SEC28 377 Emaxcont sing_1398.htm#SEC1474 47312 378 Enumerative geometry sing_2695.htm#IDX1045 379 Envelope sing_923.htm#IDX429 380 Equal sing_1352.htm#SEC1428 19984 381 Eresol sing_1388.htm#SEC1464 12842 382 EulerAff sing_2313.htm#SEC2389 54325 383 EulerProj sing_2314.htm#SEC2390 13537 374 Emaxcont sing_1400.htm#SEC1476 47312 375 Enumerative geometry sing_2702.htm#IDX1043 376 Equal sing_1354.htm#SEC1430 19984 377 Eresol sing_1390.htm#SEC1466 12842 378 EulerAff sing_2315.htm#SEC2391 54325 379 EulerProj sing_2316.htm#SEC2392 13537 384 380 Evaluation of logical expressions Evaluation of logical expressions sing_411.htm#SEC451 385 381 Examples sing_806.htm#SEC858 386 382 Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40 387 Exp for matrices sing_137 0.htm#IDX607388 Experimental libraries Experimental libraries sing_224 3.htm#SEC2319389 Ext sing_116 4.htm#SEC124021909383 Exp for matrices sing_1372.htm#IDX600 384 Experimental libraries Experimental libraries sing_2245.htm#SEC2321 385 Ext sing_1166.htm#SEC1242 21909 390 386 Ext, computation of sing_827.htm#SEC879 391 Ext_R sing_116 3.htm#SEC123953310387 Ext_R sing_1165.htm#SEC1241 53310 392 388 Exterior sing_732.htm#SEC784 23593 393 389 Extra weight vector sing_865.htm#SEC917 394 390 Factorization sing_829.htm#SEC881 395 391 FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_941.htm#SEC1017 18153 396 Feynman graph sing_114 0.htm#IDX529392 Feynman graph sing_1142.htm#IDX522 397 393 Finite fields sing_823.htm#SEC875 398 394 First steps sing_6.htm#SEC12 … … 404 400 Free resolution sing_825.htm#SEC877 405 401 Free resolution, graded Handling graded modules sing_826.htm#SEC878 406 FultonA sing_231 1.htm#SEC238733688402 FultonA sing_2313.htm#SEC2389 33688 407 403 Functions sing_207.htm#SEC247 408 Future benefits of Singular 4 Notes for Singular users sing_275 0.htm#SEC2839404 Future benefits of Singular 4 Notes for Singular users sing_2757.htm#SEC2846 409 405 G-algebra sing_486.htm#SEC526 410 406 G-algebra sing_486.htm#SEC528 411 407 G-algebra, setup sing_486.htm#SEC530 412 408 GBWeight sing_569.htm#SEC621 24641 413 GBsolve sing_170 5.htm#SEC178116830409 GBsolve sing_1707.htm#SEC1783 16830 414 410 GIT-Fans sing_848.htm#SEC900 415 GITcone sing_242 0.htm#SEC249664643416 GITfan sing_242 1.htm#SEC249732549417 GITfanFromOrbitCones GITfanFromOrbitCones sing_242 2.htm#SEC249863104418 GITfanParallel sing_242 3.htm#SEC249953071419 GITfanParallelSymmetric GITfanParallelSymmetric sing_24 38.htm#SEC251430232420 GITfanSymmetric sing_24 37.htm#SEC251325831421 GKZfan sing_24 24.htm#SEC2500sprintf411 GITcone sing_2426.htm#SEC2502 64643 412 GITfan sing_2427.htm#SEC2503 32549 413 GITfanFromOrbitCones GITfanFromOrbitCones sing_2428.htm#SEC2504 63104 414 GITfanParallel sing_2429.htm#SEC2505 53071 415 GITfanParallelSymmetric GITfanParallelSymmetric sing_2444.htm#SEC2520 30232 416 GITfanSymmetric sing_2443.htm#SEC2519 25831 417 GKZfan sing_2430.htm#SEC2506 sprintf 422 418 GKZsystem sing_698.htm#SEC750 20528 423 419 GKdim sing_671.htm#SEC723 9814 424 420 GMP sing_1.htm#IDX3 425 GMP sing_27 54.htm#SEC2843426 GND.lib sing_24 45.htm#SEC2521427 GND_lib sing_24 45.htm#SEC2521428 GTZmod sing_121 4.htm#SEC129030091429 GTZopt sing_122 1.htm#SEC129714642421 GMP sing_2761.htm#SEC2850 422 GND.lib sing_2451.htm#SEC2527 423 GND_lib sing_2451.htm#SEC2527 424 GTZmod sing_1216.htm#SEC1292 30091 425 GTZopt sing_1223.htm#SEC1299 14642 430 426 G_a -Invariants sing_845.htm#SEC897 431 Gamma sing_140 3.htm#SEC14793820427 Gamma sing_1405.htm#SEC1481 3820 432 428 Gauss-Manin connection Gauss-Manin connection sing_872.htm#SEC929 433 Gauss-Manin connection sing_158 3.htm#IDX778434 Gauss-Manin connection sing_163 0.htm#IDX781435 Gauss-Manin system sing_153 1.htm#IDX668436 Gauss-Manin system sing_153 2.htm#IDX679437 Gauss-Manin system sing_153 3.htm#IDX682438 Gauss-Manin system sing_153 4.htm#IDX685439 Gauss-Manin system sing_153 5.htm#IDX688440 Gauss-Manin system sing_153 6.htm#IDX692441 Gauss-Manin system sing_153 7.htm#IDX696442 Gauss-Manin system sing_15 38.htm#IDX702443 Gauss-Manin system sing_15 39.htm#IDX710444 Gauss-Manin system sing_154 0.htm#IDX716445 Gauss-Manin system sing_154 1.htm#IDX724446 Gauss-Manin system sing_154 2.htm#IDX734447 Gauss-Manin system sing_155 3.htm#IDX740448 Gauss-Manin system sing_155 5.htm#IDX751429 Gauss-Manin connection sing_1585.htm#IDX771 430 Gauss-Manin connection sing_1632.htm#IDX774 431 Gauss-Manin system sing_1533.htm#IDX661 432 Gauss-Manin system sing_1534.htm#IDX672 433 Gauss-Manin system sing_1535.htm#IDX675 434 Gauss-Manin system sing_1536.htm#IDX678 435 Gauss-Manin system sing_1537.htm#IDX681 436 Gauss-Manin system sing_1538.htm#IDX685 437 Gauss-Manin system sing_1539.htm#IDX689 438 Gauss-Manin system sing_1540.htm#IDX695 439 Gauss-Manin system sing_1541.htm#IDX703 440 Gauss-Manin system sing_1542.htm#IDX709 441 Gauss-Manin system sing_1543.htm#IDX717 442 Gauss-Manin system sing_1544.htm#IDX727 443 Gauss-Manin system sing_1555.htm#IDX733 444 Gauss-Manin system sing_1557.htm#IDX744 449 445 General command syntax General command syntax sing_35.htm#SEC59 450 446 General concepts sing_12.htm#SEC18 … … 454 450 Generalized Newton identities Generalized Newton identities sing_888.htm#SEC954 455 451 Geometric Invariant Theory Geometric Invariant Theory sing_847.htm#SEC899 456 Geometric genus sing_1374.htm#IDX619 452 Geometric Theorems sing_945.htm#IDX484 453 Geometric genus sing_1376.htm#IDX612 457 454 German Umlaute sing_407.htm#IDX285 458 455 Getting started sing_5.htm#SEC11 459 456 Global orderings sing_860.htm#SEC912 460 Goettsche's formula sing_2 398.htm#IDX984461 GoettscheF sing_2 399.htm#SEC247527881457 Goettsche's formula sing_2404.htm#IDX981 458 GoettscheF sing_2405.htm#SEC2481 27881 462 459 Graded commutative algebras Graded commutative algebras (SCA) sing_490.htm#SEC542 463 Grassmannian sing_270 0.htm#SEC277643898464 Grassmannian, abstract variety, Schubert calculus Grassmannian sing_270 0.htm#IDX1053460 Grassmannian sing_2707.htm#SEC2783 43898 461 Grassmannian, abstract variety, Schubert calculus Grassmannian sing_2707.htm#IDX1051 465 462 Greuel, Gert-Martin sing_1.htm#IDX18 466 463 Groebner Bases Computing Groebner and Standard Bases sing_817.htm#SEC869 467 Groebner Cover sing_923.htm#IDX423468 464 Groebner bases in G-algebras Groebner bases in G-algebras sing_487.htm#SEC531 469 465 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_493.htm#SEC545 470 Groebner bases, decodeGB sing_180 6.htm#IDX802466 Groebner bases, decodeGB sing_1808.htm#IDX795 471 467 Groebner bases, slim sing_820.htm#SEC872 472 468 Groebner basis conversion Groebner basis conversion sing_819.htm#SEC871 473 Groebner cover sing_924.htm#IDX4 31474 Groebner cover sing_931.htm#IDX4 50475 Groebner cover sing_932.htm#IDX4 57476 Groebner fan sing_20 69.htm#IDX819477 Groebner walk sing_115 5.htm#IDX550478 Groebner walk sing_115 7.htm#IDX552479 Groebner walk sing_269 2.htm#IDX1041480 Groebner walk sing_2 693.htm#IDX1042481 Groebnerwalk sing_115 1.htm#IDX546482 Groebnerwalk sing_25 37.htm#IDX994483 Groebnerwalk sing_269 1.htm#IDX1040484 Groebnerwalk sing_27 34.htm#IDX1069485 Gromov-Witten invariants sing_114 0.htm#IDX526486 Gromov-Witten invariants sing_114 6.htm#IDX535487 Gromov-Witten invariants sing_114 7.htm#IDX539488 Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_27 25.htm#IDX1065489 Gromov-Witten invariants, multiple covers sing_27 24.htm#IDX1064490 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_27 26.htm#IDX1066491 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_27 27.htm#IDX1067492 Gromov-Witten invariants. sing_2 695.htm#IDX1048469 Groebner cover sing_924.htm#IDX422 470 Groebner cover sing_931.htm#IDX441 471 Groebner cover sing_932.htm#IDX448 472 Groebner fan sing_2071.htm#IDX812 473 Groebner walk sing_1157.htm#IDX543 474 Groebner walk sing_1159.htm#IDX545 475 Groebner walk sing_2699.htm#IDX1039 476 Groebner walk sing_2700.htm#IDX1040 477 Groebnerwalk sing_1153.htm#IDX539 478 Groebnerwalk sing_2544.htm#IDX992 479 Groebnerwalk sing_2698.htm#IDX1038 480 Groebnerwalk sing_2741.htm#IDX1067 481 Gromov-Witten invariants sing_1142.htm#IDX519 482 Gromov-Witten invariants sing_1148.htm#IDX528 483 Gromov-Witten invariants sing_1149.htm#IDX532 484 Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_2732.htm#IDX1063 485 Gromov-Witten invariants, multiple covers sing_2731.htm#IDX1062 486 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_2733.htm#IDX1064 487 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_2734.htm#IDX1065 488 Gromov-Witten invariants. sing_2702.htm#IDX1046 493 489 Gweights sing_726.htm#SEC778 651 494 H2basis sing_15 88.htm#SEC16643414495 HHnormalForm sing_23 29.htm#SEC240533972496 Hamburger-Noether expansion sing_14 68.htm#IDX638497 Hamburger-Noether expansion sing_155 6.htm#IDX760498 Hamburger-Noether expansions sing_179 3.htm#IDX792490 H2basis sing_1590.htm#SEC1666 3414 491 HHnormalForm sing_2331.htm#SEC2407 33972 492 Hamburger-Noether expansion sing_1470.htm#IDX631 493 Hamburger-Noether expansion sing_1558.htm#IDX753 494 Hamburger-Noether expansions sing_1795.htm#IDX785 499 495 Handling graded modules Handling graded modules sing_826.htm#SEC878 500 Hcode sing_149 0.htm#SEC156626628496 Hcode sing_1492.htm#SEC1568 26628 501 497 Help string sing_45.htm#SEC82 502 498 Hensel sing_241.htm#SEC281 … … 505 501 Hilbert series sing_869.htm#SEC923 506 502 Hilbert-driven GB algorithm Groebner basis conversion sing_819.htm#SEC871 507 HilbertClassPoly sing_18 78.htm#SEC1954sprintf508 HilbertSeries sing_168 3.htm#SEC175921249509 HilbertWeights sing_168 4.htm#SEC1760sprintf510 Hom sing_116 7.htm#SEC124361434511 HomJJ sing_124 4.htm#SEC13201525503 HilbertClassPoly sing_1880.htm#SEC1956 sprintf 504 HilbertSeries sing_1685.htm#SEC1761 21249 505 HilbertWeights sing_1686.htm#SEC1762 sprintf 506 Hom sing_1169.htm#SEC1245 61434 507 HomJJ sing_1246.htm#SEC1322 1525 512 508 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_878.htm#SEC935 513 509 How to enter and exit How to enter and exit sing_14.htm#SEC20 514 510 How to use this manual How to use this manual sing_4.htm#SEC6 515 Hurwitz numbers sing_114 6.htm#IDX538516 Hurwitz numbers sing_114 7.htm#IDX542511 Hurwitz numbers sing_1148.htm#IDX531 512 Hurwitz numbers sing_1149.htm#IDX535 517 513 Hypersurface singularities, classification of Classification of hypersurface singularities sing_842.htm#SEC894 518 I-regular function sing_931.htm#IDX4 56514 I-regular function sing_931.htm#IDX447 519 515 IN sing_280.htm#IDX149 520 516 Ideal membership sing_868.htm#IDX418 521 517 Identifiers, syntax of sing_37.htm#SEC65 522 ImageGroup sing_168 6.htm#SEC176228808523 ImageVariety sing_168 5.htm#SEC176115252518 ImageGroup sing_1688.htm#SEC1764 28808 519 ImageVariety sing_1687.htm#SEC1763 15252 524 520 Imap, option sing_315.htm#IDX175 525 521 Implemented algorithms Implemented algorithms sing_33.htm#SEC47 526 Incl sing_135 1.htm#SEC14277621527 Index sing_27 59.htm#SEC2848522 Incl sing_1353.htm#SEC1429 7621 523 Index sing_2766.htm#SEC2855 528 524 Info string sing_52.htm#SEC89 529 InterDiv sing_14 19.htm#SEC149546142525 InterDiv sing_1421.htm#SEC1497 46142 530 526 Interactive use sing_13.htm#SEC19 531 527 Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24 532 528 IntersectWithSub sing_703.htm#SEC755 56289 533 Intersection theory sing_2 695.htm#IDX1044534 IntersectionMatrix sing_151 7.htm#SEC159329351529 Intersection theory sing_2702.htm#IDX1042 530 IntersectionMatrix sing_1519.htm#SEC1595 29351 535 531 Introduction sing_2.htm#SEC4 536 532 Invariant Theory sing_844.htm#SEC896 537 Invariant theory sing_163 5.htm#SEC1711538 InvariantQ sing_16 88.htm#SEC176453256539 InvariantRing sing_168 7.htm#SEC176322928533 Invariant theory sing_1637.htm#SEC1713 534 InvariantQ sing_1690.htm#SEC1766 53256 535 InvariantRing sing_1689.htm#SEC1765 22928 540 536 Invariants of a finite group Invariants of a finite group sing_846.htm#SEC898 541 537 Invariants of plane curve singularities Invariants of plane curve singularities sing_840.htm#SEC892 542 538 IsSCA sing_747.htm#SEC799 58445 543 J-marked schemes sing_14 59.htm#IDX636544 J-marked schemes, Borel ideals sing_146 4.htm#IDX637545 JMBTest.lib sing_14 59.htm#SEC1535546 JMBTest_lib sing_14 59.htm#SEC1535547 JMSConst.lib sing_146 4.htm#SEC1540548 JMSConst_lib sing_146 4.htm#SEC1540549 JMarkedScheme sing_146 6.htm#SEC154260696550 Jacobi sing_18 88.htm#SEC196429843551 Jacobson form sing_184 3.htm#IDX803552 Jacobson normal form sing_184 3.htm#IDX804553 Janet basis sing_269 0.htm#IDX1038554 Janet division, Janet basis sing_26 89.htm#IDX1037555 JuReTopDim sing_136 1.htm#SEC1437sprintf556 JuReZeroDim sing_136 2.htm#SEC1438sprintf557 KScoef sing_158 1.htm#SEC1657sprintf558 KSconvert sing_15 79.htm#SEC16553585559 KSker sing_15 78.htm#SEC165440166560 KSlinear sing_158 0.htm#SEC165619896561 KSpencerKernel sing_16 28.htm#SEC170412490562 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_24 64.htm#SEC254020741563 Ker sing_25 09.htm#SEC258558279539 J-marked schemes sing_1461.htm#IDX629 540 J-marked schemes, Borel ideals sing_1466.htm#IDX630 541 JMBTest.lib sing_1461.htm#SEC1537 542 JMBTest_lib sing_1461.htm#SEC1537 543 JMSConst.lib sing_1466.htm#SEC1542 544 JMSConst_lib sing_1466.htm#SEC1542 545 JMarkedScheme sing_1468.htm#SEC1544 60696 546 Jacobi sing_1890.htm#SEC1966 29843 547 Jacobson form sing_1845.htm#IDX796 548 Jacobson normal form sing_1845.htm#IDX797 549 Janet basis sing_2697.htm#IDX1036 550 Janet division, Janet basis sing_2696.htm#IDX1035 551 JuReTopDim sing_1363.htm#SEC1439 sprintf 552 JuReZeroDim sing_1364.htm#SEC1440 sprintf 553 KScoef sing_1583.htm#SEC1659 sprintf 554 KSconvert sing_1581.htm#SEC1657 3585 555 KSker sing_1580.htm#SEC1656 40166 556 KSlinear sing_1582.htm#SEC1658 19896 557 KSpencerKernel sing_1630.htm#SEC1706 12490 558 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2470.htm#SEC2546 20741 559 Ker sing_2516.htm#SEC2592 58279 564 560 Kernel of module homomorphisms Kernel of module homomorphisms sing_832.htm#SEC884 565 KoszulHomology sing_117 6.htm#SEC1252sprintf566 Kronecker modules sing_2 398.htm#IDX986561 KoszulHomology sing_1178.htm#SEC1254 sprintf 562 Kronecker modules sing_2404.htm#IDX983 567 563 L, ordering sing_866.htm#SEC918 568 564 LETTERPLACE sing_491.htm#SEC543 … … 573 569 LOT algorithm sing_540.htm#IDX340 574 570 LU-decomposition of a matrix of numbers sing_289.htm#SEC329 575 Laurent series sing_114 4.htm#IDX534571 Laurent series sing_1146.htm#IDX527 576 572 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_850.htm#SEC902 577 573 Left ideal membership Groebner bases in G-algebras sing_487.htm#SEC534 … … 580 576 LengthSymElement sing_756.htm#SEC808 28292 581 577 Letterplace sing_491.htm#SEC543 578 Levels sing_934.htm#SEC1010 16031 582 579 Lexicographic Groebner bases, computation of Groebner basis conversion sing_819.htm#SEC871 583 580 Libraries Writing procedures and libraries sing_48.htm#SEC85 584 581 Libraries sing_809.htm#SEC861 585 582 Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86 586 Library versioning Notes for Singular users sing_275 0.htm#SEC2837587 Lie algebra sing_13 69.htm#IDX604588 Lie group sing_137 2.htm#IDX609589 Lie group sing_137 3.htm#IDX612583 Library versioning Notes for Singular users sing_2757.htm#SEC2844 584 Lie algebra sing_1371.htm#IDX597 585 Lie group sing_1374.htm#IDX602 586 Lie group sing_1375.htm#IDX605 590 587 Limitations sing_407.htm#SEC447 591 Linear algebra sing_104 4.htm#SEC1120592 Linear code sing_180 6.htm#IDX799593 LinearActionQ sing_169 0.htm#SEC176662218594 LinearCombinationQ sing_169 1.htm#SEC176759373595 LinearizeAction sing_16 89.htm#SEC176560266588 Linear algebra sing_1046.htm#SEC1122 589 Linear code sing_1808.htm#IDX792 590 LinearActionQ sing_1692.htm#SEC1768 62218 591 LinearCombinationQ sing_1693.htm#SEC1769 59373 592 LinearizeAction sing_1691.htm#SEC1767 60266 596 593 Loading a library sing_62.htm#SEC99 597 594 Local orderings sing_861.htm#SEC913 598 Loci sing_923.htm#IDX428 599 Log for matrices sing_1371.htm#IDX608 595 Log for matrices sing_1373.htm#IDX601 600 596 Long coefficients sing_811.htm#SEC863 601 597 M, ordering sing_863.htm#SEC915 602 MVComplex sing_23 47.htm#SEC242362126603 Macdonald's formula sing_2 398.htm#IDX985604 MacdonaldF sing_240 2.htm#SEC247812751605 Macintosh installation Macintosh installation instructions sing_27 58.htm#SEC2847598 MVComplex sing_2353.htm#SEC2429 62126 599 Macdonald's formula sing_2404.htm#IDX982 600 MacdonaldF sing_2408.htm#SEC2484 12751 601 Macintosh installation Macintosh installation instructions sing_2765.htm#SEC2854 606 602 Mathematical background Mathematical background sing_867.htm#SEC919 607 603 Mathematical background (plural) Mathematical background (plural) sing_485.htm#SEC525 608 604 Matrix orderings sing_863.htm#SEC915 609 Max sing_159 7.htm#SEC167323610 Maximus sing_146 1.htm#SEC153710010611 Maxord sing_140 2.htm#SEC147814124612 MillerRabin sing_1 898.htm#SEC197415740605 Max sing_1599.htm#SEC1675 23 606 Maximus sing_1463.htm#SEC1539 10010 607 Maxord sing_1404.htm#SEC1480 14124 608 MillerRabin sing_1900.htm#SEC1976 15740 613 609 Milnor number Milnor and Tjurina number sing_835.htm#SEC887 614 Milnor number sing_267 0.htm#IDX1026615 Min sing_1 598.htm#SEC167429622616 MinMult sing_231 7.htm#SEC239339835617 MinimalDecomposition MinimalDecomposition sing_169 2.htm#SEC176824161618 Minimum distance sing_180 6.htm#IDX801619 Minimus sing_146 0.htm#SEC153661721620 Miscellaneous libraries Miscellaneous libraries sing_217 0.htm#SEC2246621 ModEqn sing_159 1.htm#SEC166759394622 Modular techniques sing_95 4.htm#IDX493610 Milnor number sing_2677.htm#IDX1024 611 Min sing_1600.htm#SEC1676 29622 612 MinMult sing_2319.htm#SEC2395 39835 613 MinimalDecomposition MinimalDecomposition sing_1694.htm#SEC1770 24161 614 Minimum distance sing_1808.htm#IDX794 615 Minimus sing_1462.htm#SEC1538 61721 616 Miscellaneous libraries Miscellaneous libraries sing_2172.htm#SEC2248 617 ModEqn sing_1593.htm#SEC1669 59394 618 Modular techniques sing_956.htm#IDX486 623 619 Module orderings sing_862.htm#SEC914 624 620 Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16 625 Monodromy sing_158 3.htm#IDX776621 Monodromy sing_1585.htm#IDX769 626 622 Monomial orderings sing_857.htm#SEC909 627 623 Monomial orderings, Term orderings sing_31.htm#SEC44 628 Mori dream spaces sing_224 4.htm#IDX941629 Morse lemma addnondegeneratevariables sing_26 69.htm#IDX1024630 Morse lemma sing_267 2.htm#IDX1028631 MultiplicitySequence MultiplicitySequence sing_151 5.htm#SEC15911309624 Mori dream spaces sing_2246.htm#IDX934 625 Morse lemma addnondegeneratevariables sing_2676.htm#IDX1022 626 Morse lemma sing_2679.htm#IDX1026 627 MultiplicitySequence MultiplicitySequence sing_1517.htm#SEC1593 1309 632 628 NF sing_334.htm#SEC374 633 629 NF sing_477.htm#SEC517 634 NFMora sing_196 4.htm#SEC204040670635 NPos sing_123 4.htm#SEC131015702636 NPos_test sing_123 2.htm#SEC130848172637 NSplaces sing_179 4.htm#SEC187048675630 NFMora sing_1966.htm#SEC2042 40670 631 NPos sing_1236.htm#SEC1312 15702 632 NPos_test sing_1234.htm#SEC1310 48172 633 NSplaces sing_1796.htm#SEC1872 48675 638 634 NTL sing_1.htm#IDX4 639 635 Names sing_37.htm#SEC65 640 636 Names in procedures sing_46.htm#SEC83 641 637 Names, indexed sing_37.htm#SEC65 642 New orderings for modules Notes for Singular users sing_275 0.htm#SEC2838643 Newton non-degenerate sing_157 0.htm#IDX774644 Newton polygon sing_15 69.htm#IDX773645 Newton polygon sing_157 0.htm#IDX775646 Newton polygons sing_27 37.htm#IDX1072647 Newton polytope sing_20 69.htm#IDX818648 Newton step sing_26 73.htm#IDX1032649 NoetherPosition sing_12 28.htm#SEC130418735638 New orderings for modules Notes for Singular users sing_2757.htm#SEC2845 639 Newton non-degenerate sing_1572.htm#IDX767 640 Newton polygon sing_1571.htm#IDX766 641 Newton polygon sing_1572.htm#IDX768 642 Newton polygons sing_2744.htm#IDX1070 643 Newton polytope sing_2071.htm#IDX811 644 Newton step sing_2680.htm#IDX1030 645 NoetherPosition sing_1230.htm#SEC1306 18735 650 646 Non-commutative LIBs Non-commutative libraries sing_497.htm#SEC549 651 647 Non-commutative algebra Non-commutative algebra sing_849.htm#SEC901 … … 653 649 Non-commutative libraries Non-commutative libraries sing_497.htm#SEC549 654 650 Non-commutative subsystem Non-commutative subsystem sing_420.htm#SEC460 655 Nonhyp sing_139 1.htm#SEC1467sprintf651 Nonhyp sing_1393.htm#SEC1469 sprintf 656 652 Normalization sing_831.htm#SEC883 657 Notes for Singular users Notes for Singular users sing_275 0.htm#SEC2833658 Notes for developers Notes for developers sing_275 1.htm#SEC2840659 NullCone sing_169 3.htm#SEC176964635660 NumIrrDecom sing_136 5.htm#SEC1441sprintf661 NumLocalDim sing_135 4.htm#SEC14301739662 NumPrimDecom sing_136 7.htm#SEC144334134653 Notes for Singular users Notes for Singular users sing_2757.htm#SEC2840 654 Notes for developers Notes for developers sing_2758.htm#SEC2847 655 NullCone sing_1695.htm#SEC1771 64635 656 NumIrrDecom sing_1367.htm#SEC1443 sprintf 657 NumLocalDim sing_1356.htm#SEC1432 1739 658 NumPrimDecom sing_1369.htm#SEC1445 34134 663 659 Oaku-Takayama algorithm sing_540.htm#IDX338 664 660 Objects sing_38.htm#SEC66 665 Orlik-Solomon sing_220 0.htm#IDX882666 Output sing_25 19.htm#IDX992667 Output sing_26 16.htm#IDX999668 Output sing_26 18.htm#IDX1000669 Output sing_26 19.htm#IDX1001670 Output sing_262 0.htm#IDX1002671 Output sing_262 1.htm#IDX1003672 Output sing_262 2.htm#IDX1004673 Output sing_26 23.htm#IDX1005674 Output sing_26 24.htm#IDX1006675 Output sing_26 25.htm#IDX1007676 Output sing_26 26.htm#IDX1008677 Output sing_26 27.htm#IDX1009678 Output sing_26 28.htm#IDX1010679 Output sing_26 29.htm#IDX1011680 Output sing_263 0.htm#IDX1012681 Output sing_263 1.htm#IDX1013682 Output sing_263 2.htm#IDX1014683 Output sing_26 33.htm#IDX1015684 Output sing_26 34.htm#IDX1016685 Output sing_26 35.htm#IDX1017686 Output sing_26 36.htm#IDX1018687 Output sing_26 37.htm#IDX1019688 Output sing_26 38.htm#IDX1020689 Output sing_26 39.htm#IDX1021690 Output sing_264 0.htm#IDX1022661 Orlik-Solomon sing_2202.htm#IDX875 662 Output sing_2526.htm#IDX990 663 Output sing_2623.htm#IDX997 664 Output sing_2625.htm#IDX998 665 Output sing_2626.htm#IDX999 666 Output sing_2627.htm#IDX1000 667 Output sing_2628.htm#IDX1001 668 Output sing_2629.htm#IDX1002 669 Output sing_2630.htm#IDX1003 670 Output sing_2631.htm#IDX1004 671 Output sing_2632.htm#IDX1005 672 Output sing_2633.htm#IDX1006 673 Output sing_2634.htm#IDX1007 674 Output sing_2635.htm#IDX1008 675 Output sing_2636.htm#IDX1009 676 Output sing_2637.htm#IDX1010 677 Output sing_2638.htm#IDX1011 678 Output sing_2639.htm#IDX1012 679 Output sing_2640.htm#IDX1013 680 Output sing_2641.htm#IDX1014 681 Output sing_2642.htm#IDX1015 682 Output sing_2643.htm#IDX1016 683 Output sing_2644.htm#IDX1017 684 Output sing_2645.htm#IDX1018 685 Output sing_2646.htm#IDX1019 686 Output sing_2647.htm#IDX1020 691 687 Output, formatting of sing_813.htm#SEC865 692 688 PBW sing_519.htm#IDX326 … … 695 691 PBW_maxDeg sing_538.htm#SEC590 59566 696 692 PBW_maxMonom sing_539.htm#SEC591 1155 697 PEsolve sing_170 3.htm#SEC17799229698 PH_ais sing_222 2.htm#SEC229849473699 PH_nais sing_222 3.htm#SEC229946271693 PEsolve sing_1705.htm#SEC1781 9229 694 PH_ais sing_2224.htm#SEC2300 49473 695 PH_nais sing_2225.htm#SEC2301 46271 700 696 PLURAL sing_421.htm#SEC461 701 697 PLURAL LIBs Non-commutative libraries sing_497.htm#SEC549 702 PPolyH sing_240 0.htm#SEC247625241703 PPolyN sing_24 05.htm#SEC248139067704 PPolyS sing_240 3.htm#SEC247913817705 ParToVar sing_2 395.htm#SEC247113991698 PPolyH sing_2406.htm#SEC2482 25241 699 PPolyN sing_2411.htm#SEC2487 39067 700 PPolyS sing_2409.htm#SEC2485 13817 701 ParToVar sing_2401.htm#SEC2477 13991 706 702 Parallelization Parallelization with ssi links sing_815.htm#SEC867 707 Parallelization sing_95 4.htm#IDX494703 Parallelization sing_956.htm#IDX487 708 704 Parameter list sing_44.htm#SEC81 709 705 Parameters sing_812.htm#SEC864 710 Parametric Polynomial Systems sing_923.htm#IDX425 711 Parametrization sing_1374.htm#IDX616 712 Parametrization, image. sing_1384.htm#IDX628 713 PartC sing_2307.htm#SEC2383 54120 714 PartitionVar sing_2392.htm#SEC2468 41350 715 Path names Notes for Singular users sing_2750.htm#SEC2836 716 PerfectPowerTest sing_1861.htm#SEC1937 17450 717 Perturbation walk sing_1156.htm#IDX551 706 Parametrization sing_1376.htm#IDX609 707 Parametrization, image. sing_1386.htm#IDX621 708 PartC sing_2309.htm#SEC2385 54120 709 PartitionVar sing_2398.htm#SEC2474 41350 710 Path names Notes for Singular users sing_2757.htm#SEC2843 711 PerfectPowerTest sing_1863.htm#SEC1939 17450 712 Perturbation walk sing_1158.htm#IDX544 718 713 Pfister, Gerhard sing_1.htm#IDX19 719 714 Pipe links sing_121.htm#SEC161 720 PocklingtonLehmer sing_190 0.htm#SEC197613634721 Poincare polynomial sing_221 2.htm#IDX906715 PocklingtonLehmer sing_1902.htm#SEC1978 13634 716 Poincare polynomial sing_2214.htm#IDX899 722 717 Polar curves sing_837.htm#SEC889 723 PollardRho sing_190 1.htm#SEC197749602724 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_222 5.htm#IDX922725 PolyBoRi, Boolean Groebner Basis sing_222 7.htm#IDX923726 PolyBoRi, Boolean Groebner Basis sing_22 28.htm#IDX924727 PolyBoRi, Boolean Groebner Basis sing_22 29.htm#IDX925728 PolyBoRi, Boolean Groebner Basis sing_223 0.htm#IDX926729 PolyBoRi, Boolean Groebner Basis sing_223 1.htm#IDX927730 PolyBoRi, Boolean Groebner Basis sing_223 2.htm#IDX928731 PolyBoRi, Boolean Groebner Basis sing_223 3.htm#IDX929732 PolyBoRi, Boolean Groebner Basis sing_223 4.htm#IDX930733 PolyBoRi, Boolean Groebner Basis sing_223 5.htm#IDX931734 PolyBoRi, Boolean Groebner Basis sing_223 6.htm#IDX932735 PolyBoRi, Boolean Groebner Basis sing_223 7.htm#IDX933736 PolyBoRi, Boolean Groebner Basis sing_22 38.htm#IDX934737 PolyBoRi, Boolean Groebner Basis sing_22 39.htm#IDX935738 PolyBoRi, Boolean Groebner Basis sing_224 1.htm#IDX937739 PolyBoRi, zero-supressed decision diagram sing_224 0.htm#IDX936740 Polybori, Boolean Groebner Basis sing_224 2.htm#IDX938718 PollardRho sing_1903.htm#SEC1979 49602 719 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2227.htm#IDX915 720 PolyBoRi, Boolean Groebner Basis sing_2229.htm#IDX916 721 PolyBoRi, Boolean Groebner Basis sing_2230.htm#IDX917 722 PolyBoRi, Boolean Groebner Basis sing_2231.htm#IDX918 723 PolyBoRi, Boolean Groebner Basis sing_2232.htm#IDX919 724 PolyBoRi, Boolean Groebner Basis sing_2233.htm#IDX920 725 PolyBoRi, Boolean Groebner Basis sing_2234.htm#IDX921 726 PolyBoRi, Boolean Groebner Basis sing_2235.htm#IDX922 727 PolyBoRi, Boolean Groebner Basis sing_2236.htm#IDX923 728 PolyBoRi, Boolean Groebner Basis sing_2237.htm#IDX924 729 PolyBoRi, Boolean Groebner Basis sing_2238.htm#IDX925 730 PolyBoRi, Boolean Groebner Basis sing_2239.htm#IDX926 731 PolyBoRi, Boolean Groebner Basis sing_2240.htm#IDX927 732 PolyBoRi, Boolean Groebner Basis sing_2241.htm#IDX928 733 PolyBoRi, Boolean Groebner Basis sing_2243.htm#IDX930 734 PolyBoRi, zero-supressed decision diagram sing_2242.htm#IDX929 735 Polybori, Boolean Groebner Basis sing_2244.htm#IDX931 741 736 Polynomial data sing_855.htm#SEC907 742 737 Pottier algorithm sing_877.htm#SEC934 743 738 Preface sing_1.htm#SEC1 744 Prep sing_929.htm#SEC1005 61895739 Prep sing_929.htm#SEC1005 55342 745 740 Primary decomposition Primary decomposition sing_830.htm#SEC882 746 PrimdecA sing_121 0.htm#SEC1286248747 PrimdecB sing_121 1.htm#SEC12879653741 PrimdecA sing_1212.htm#SEC1288 248 742 PrimdecB sing_1213.htm#SEC1289 9653 748 743 Procedure definition Procedure definition sing_43.htm#SEC78 749 744 Procedure-specific commands Procedure-specific commands sing_47.htm#SEC84 … … 755 750 Programming sing_807.htm#SEC859 756 751 Pseudo ordering L sing_866.htm#SEC918 757 PtoCrep sing_930.htm#SEC1006 11462758 Puiseux expansion sing_14 68.htm#IDX639759 Puiseux expansion sing_155 6.htm#IDX761752 PtoCrep sing_930.htm#SEC1006 52961 753 Puiseux expansion sing_1470.htm#IDX632 754 Puiseux expansion sing_1558.htm#IDX754 760 755 Puiseux pairs Invariants of plane curve singularities sing_840.htm#SEC892 761 Puiseux pairs sing_156 2.htm#IDX766756 Puiseux pairs sing_1564.htm#IDX759 762 757 QQ sing_28.htm#SEC39 763 758 Qso3Casimir sing_697.htm#SEC749 40212 764 Quotient sing_174 5.htm#SEC182124888765 QuotientEquations sing_159 2.htm#SEC166818230766 Rational curves sing_137 4.htm#IDX617767 ReJunkUseHomo sing_136 0.htm#SEC143610186768 ReesAlgebra sing_132 7.htm#SEC140359951759 Quotient sing_1747.htm#SEC1823 24888 760 QuotientEquations sing_1594.htm#SEC1670 18230 761 Rational curves sing_1376.htm#IDX610 762 ReJunkUseHomo sing_1362.htm#SEC1438 10186 763 ReesAlgebra sing_1329.htm#SEC1405 59951 769 764 References sing_892.htm#SEC966 770 765 References (plural) sing_489.htm#SEC539 771 Release Notes sing_27 46.htm#SEC2822772 Res sing_2 499.htm#SEC257592773 ResTree sing_142 0.htm#SEC149658727766 Release Notes sing_2753.htm#SEC2829 767 Res sing_2506.htm#SEC2582 92 768 ResTree sing_1422.htm#SEC1498 58727 774 769 Resolution sing_11.htm#SEC17 775 770 Resolution of singularities Resolution of singularities sing_843.htm#SEC895 776 771 Resolution, free sing_825.htm#SEC877 777 ReynoldsImage sing_169 4.htm#SEC177035172778 ReynoldsOperator sing_169 5.htm#SEC177114986779 RiemannRochBN sing_225 2.htm#SEC232820085780 RiemannRochHess sing_248 3.htm#SEC2559sprintf772 ReynoldsImage sing_1696.htm#SEC1772 35172 773 ReynoldsOperator sing_1697.htm#SEC1773 14986 774 RiemannRochBN sing_2254.htm#SEC2330 20085 775 RiemannRochHess sing_2489.htm#SEC2565 sprintf 781 776 Right Groebner bases and syzygies Right Groebner bases and syzygies sing_851.htm#SEC903 782 Ring-dependent options Notes for Singular users sing_275 0.htm#SEC2835777 Ring-dependent options Notes for Singular users sing_2757.htm#SEC2842 783 778 Rings and orderings sing_28.htm#SEC39 784 779 Rings and standard bases Rings and standard bases sing_7.htm#SEC13 … … 790 785 SINGULAR libraries sing_893.htm#SEC969 791 786 SINGULARHIST sing_18.htm#SEC25 792 SV-decoding algorithm sing_180 1.htm#IDX795793 SV-decoding algorithm, preprocessing sing_180 0.htm#IDX794787 SV-decoding algorithm sing_1803.htm#IDX788 788 SV-decoding algorithm, preprocessing sing_1802.htm#IDX787 794 789 Sannfs sing_543.htm#SEC595 42932 795 790 SannfsBFCT sing_552.htm#SEC604 59702 … … 797 792 Sannfslog sing_544.htm#SEC596 49313 798 793 Saturation sing_822.htm#SEC874 799 Saturation sing_113 7.htm#IDX520794 Saturation sing_1139.htm#IDX513 800 795 Sch@"onemann, Hans sing_1.htm#IDX20 801 Schoof sing_191 2.htm#SEC198849281802 Schubert calculus sing_2 695.htm#IDX1046803 SchubertClass sing_273 2.htm#SEC280862336804 SchurCh sing_230 4.htm#SEC238058575805 SchurS sing_230 3.htm#SEC237946004806 SegreA sing_231 0.htm#SEC238655776807 Semigroup sing_15 08.htm#SEC158422323808 SetDeg sing_250 2.htm#SEC257840547796 Schoof sing_1914.htm#SEC1990 49281 797 Schubert calculus sing_2702.htm#IDX1044 798 SchubertClass sing_2739.htm#SEC2815 62336 799 SchurCh sing_2306.htm#SEC2382 58575 800 SchurS sing_2305.htm#SEC2381 46004 801 SegreA sing_2312.htm#SEC2388 55776 802 Semigroup sing_1510.htm#SEC1586 22323 803 SetDeg sing_2509.htm#SEC2585 40547 809 804 Setting up a G-algebra sing_486.htm#SEC530 810 ShanksMestre sing_191 1.htm#SEC198712973811 SimplifyIdeal sing_169 6.htm#SEC1772sprintf805 ShanksMestre sing_1913.htm#SEC1989 12973 806 SimplifyIdeal sing_1698.htm#SEC1774 sprintf 812 807 Singular sing_358.htm#IDX257 813 Singular 3 and Singular 4 Singular 3 and Singular 4 sing_27 48.htm#SEC2831808 Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2755.htm#SEC2838 814 809 Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC36 815 810 Singular, demo mode sing_24.htm#SEC35 … … 817 812 Singular, important commands of Emacs interface Top 20 Emacs commands sing_27.htm#SEC38 818 813 Singular, running within Emacs Running SINGULAR under Emacs sing_23.htm#SEC30 819 Singular2bertini sing_13 58.htm#SEC14347552814 Singular2bertini sing_1360.htm#SEC1436 7552 820 815 SingularLib sing_358.htm#IDX259 821 Singularities sing_146 7.htm#SEC1543816 Singularities sing_1469.htm#SEC1545 822 817 Singularity Theory sing_834.htm#SEC886 823 Skeletons for parallelization sing_95 4.htm#IDX495824 Smith form sing_184 3.htm#IDX805825 Smith normal form sing_184 3.htm#IDX806826 SolowayStrassen sing_1 899.htm#SEC197522680818 Skeletons for parallelization sing_956.htm#IDX488 819 Smith form sing_1845.htm#IDX798 820 Smith normal form sing_1845.htm#IDX799 821 SolowayStrassen sing_1901.htm#SEC1977 22680 827 822 Solving systems of polynomial equations Solving systems of polynomial equations sing_853.htm#SEC905 828 Source sing_249 1.htm#SEC256710351823 Source sing_2498.htm#SEC2574 10351 829 824 Source code debugger, invocation Command line options sing_19.htm#IDX33 830 825 Space curve singularities, branches of Branches of space curve singularities sing_841.htm#SEC893 831 826 Special characters sing_36.htm#SEC64 832 Splitting lemma addnondegeneratevariables sing_26 69.htm#IDX1025833 Splitting lemma sing_267 2.htm#IDX1029827 Splitting lemma addnondegeneratevariables sing_2676.htm#IDX1023 828 Splitting lemma sing_2679.htm#IDX1027 834 829 Ssi file links sing_119.htm#SEC159 835 830 Ssi links sing_118.htm#SEC158 836 831 Ssi tcp links sing_120.htm#SEC160 837 StabEqn sing_159 3.htm#SEC166928539838 StabEqnId sing_159 4.htm#SEC167027955839 StabOrder sing_159 5.htm#SEC167155603832 StabEqn sing_1595.htm#SEC1671 28539 833 StabEqnId sing_1596.htm#SEC1672 27955 834 StabOrder sing_1597.htm#SEC1673 55603 840 835 Standard Bases Computing Groebner and Standard Bases sing_817.htm#SEC869 841 836 Standard bases sing_868.htm#SEC920 842 StartOrderingV sing_146 2.htm#SEC153858927837 StartOrderingV sing_1464.htm#SEC1540 58927 843 838 Startup sequence sing_20.htm#SEC27 844 StringF sing_158 2.htm#SEC165811590839 StringF sing_1584.htm#SEC1660 11590 845 840 SymGroup sing_755.htm#SEC807 56676 846 841 Symbolic-numerical solving Symbolic-numerical solving sing_853.htm#SEC905 847 Symbolic-numerical solving sing_170 0.htm#SEC1776848 System and Control theory System and Control theory sing_182 5.htm#SEC1901842 Symbolic-numerical solving sing_1702.htm#SEC1778 843 System and Control theory System and Control theory sing_1827.htm#SEC1903 849 844 System dependent limitations System dependent limitations sing_408.htm#SEC448 850 845 System variables sing_394.htm#SEC434 … … 855 850 TRACE Tracing of procedures sing_65.htm#SEC102 856 851 TRACE sing_403.htm#SEC443 857 T_1 sing_161 5.htm#SEC169159277858 T_12 sing_161 7.htm#SEC169312923859 T_2 sing_161 6.htm#SEC169255781860 Target sing_249 0.htm#SEC256616006861 Teaching sing_185 7.htm#SEC1933852 T_1 sing_1617.htm#SEC1693 59277 853 T_12 sing_1619.htm#SEC1695 12923 854 T_2 sing_1618.htm#SEC1694 55781 855 Target sing_2497.htm#SEC2573 16006 856 Teaching sing_1859.htm#SEC1935 862 857 Template for writing a library sing_55.htm#SEC92 863 TestGRRes sing_246 3.htm#SEC25398315864 TestJMark sing_146 3.htm#SEC153941314858 TestGRRes sing_2469.htm#SEC2545 8315 859 TestJMark sing_1465.htm#SEC1541 41314 865 860 The SINGULAR language The SINGULAR language sing_34.htm#SEC56 866 The Tran algorithm sing_115 3.htm#IDX548867 The fractal walk algorithm sing_115 2.htm#IDX547868 The fractal walk algorithm sing_2 694.htm#IDX1043861 The Tran algorithm sing_1155.htm#IDX541 862 The fractal walk algorithm sing_1154.htm#IDX540 863 The fractal walk algorithm sing_2701.htm#IDX1041 869 864 The online help system The online help system sing_16.htm#SEC22 870 Tjurina sing_161 3.htm#SEC168911249865 Tjurina sing_1615.htm#SEC1691 11249 871 866 Tjurina number Milnor and Tjurina number sing_835.htm#SEC887 872 Tjurina number sing_12 49.htm#IDX577867 Tjurina number sing_1251.htm#IDX570 873 868 Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38 874 Tor sing_11 78.htm#SEC1254sprintf869 Tor sing_1180.htm#SEC1256 sprintf 875 870 Toric ideals and integer programming Toric ideals and integer programming sing_873.htm#SEC930 876 871 Tricks and pitfalls sing_406.htm#SEC446 877 Tropical Geometry sing_20 09.htm#SEC2085872 Tropical Geometry sing_2011.htm#SEC2087 878 873 Type casting Type conversion and casting sing_39.htm#SEC69 879 874 Type conversion Type conversion and casting sing_39.htm#SEC68 880 875 Typesetting of help and info strings Typesetting of help and info strings sing_61.htm#SEC98 881 U_D_O sing_109 3.htm#SEC116926192882 Unix installation Unix installation instructions sing_27 56.htm#SEC2845876 U_D_O sing_1095.htm#SEC1171 26192 877 Unix installation Unix installation instructions sing_2763.htm#SEC2852 883 878 UpOneMatrix sing_744.htm#SEC796 63020 884 UpperMonomials sing_159 6.htm#SEC167220941885 UseBertini sing_135 7.htm#SEC143343362879 UpperMonomials sing_1598.htm#SEC1674 20941 880 UseBertini sing_1359.htm#SEC1435 43362 886 881 User defined types sing_182.htm#SEC222 887 V-filtration sing_153 1.htm#IDX671888 V-filtration sing_153 7.htm#IDX699889 V-filtration sing_15 38.htm#IDX705890 V-filtration sing_15 39.htm#IDX713891 V-filtration sing_154 0.htm#IDX719892 V-filtration sing_154 1.htm#IDX727893 V-filtration sing_154 2.htm#IDX737894 V-filtration sing_155 3.htm#IDX743895 V-filtration sing_155 5.htm#IDX754896 VarToPar sing_2 394.htm#SEC247010508882 V-filtration sing_1533.htm#IDX664 883 V-filtration sing_1539.htm#IDX692 884 V-filtration sing_1540.htm#IDX698 885 V-filtration sing_1541.htm#IDX706 886 V-filtration sing_1542.htm#IDX712 887 V-filtration sing_1543.htm#IDX720 888 V-filtration sing_1544.htm#IDX730 889 V-filtration sing_1555.htm#IDX736 890 V-filtration sing_1557.htm#IDX747 891 VarToPar sing_2400.htm#SEC2476 10508 897 892 Variables, indexed sing_37.htm#SEC65 898 Version number Version schema for Singular sing_27 49.htm#SEC2832899 Version schema for Singular Version schema for Singular sing_27 49.htm#SEC2832893 Version number Version schema for Singular sing_2756.htm#SEC2839 894 Version schema for Singular Version schema for Singular sing_2756.htm#SEC2839 900 895 Version string sing_50.htm#SEC87 901 Visualization sing_176 3.htm#SEC1839896 Visualization sing_1765.htm#SEC1841 902 897 WLemma sing_943.htm#SEC1019 7302 903 898 WP, global ordering sing_860.htm#IDX400 904 WSemigroup sing_151 3.htm#SEC158957449905 Weierstrass sing_179 6.htm#SEC187258220906 Weierstrass semigroup sing_179 2.htm#IDX789899 WSemigroup sing_1515.htm#SEC1591 57449 900 Weierstrass sing_1798.htm#SEC1874 58220 901 Weierstrass semigroup sing_1794.htm#IDX782 907 902 Weyl sing_729.htm#SEC781 29212 908 903 Weyl algebra sing_540.htm#IDX332 … … 911 906 WeylClosure sing_782.htm#SEC834 23845 912 907 WeylClosure1 sing_783.htm#SEC835 15759 913 Wibmer's Lemma sing_943.htm#IDX4 91914 Windows installation Windows installation instructions sing_27 57.htm#SEC2846915 WitSet sing_136 4.htm#SEC144039803916 WitSupSet sing_136 3.htm#SEC143947758908 Wibmer's Lemma sing_943.htm#IDX481 909 Windows installation Windows installation instructions sing_2764.htm#SEC2853 910 WitSet sing_1366.htm#SEC1442 39803 911 WitSupSet sing_1365.htm#SEC1441 47758 917 912 Ws, local ordering sing_861.htm#IDX412 918 XLsolve sing_170 6.htm#SEC178234970913 XLsolve sing_1708.htm#SEC1784 34970 919 914 ZZ sing_28.htm#SEC39 920 915 ZZ/m sing_28.htm#SEC39 921 916 ZZ/p sing_28.htm#SEC39 922 ZZsolve sing_170 7.htm#SEC178318657917 ZZsolve sing_1709.htm#SEC1785 18657 923 918 [ sing_36.htm#IDX83 924 919 [] sing_142.htm#SEC182 … … 936 931 ` sing_36.htm#IDX105 937 932 a, ordering sing_865.htm#SEC917 938 absFactorize sing_110 6.htm#SEC118252546939 absFactorizeBCG sing_110 7.htm#SEC118355510940 absPrimdecGTZ sing_130 7.htm#SEC138346393941 absPrimdecGTZE sing_13 08.htm#SEC138448005933 absFactorize sing_1108.htm#SEC1184 52546 934 absFactorizeBCG sing_1109.htm#SEC1185 55510 935 absPrimdecGTZ sing_1309.htm#SEC1385 46393 936 absPrimdecGTZE sing_1310.htm#SEC1386 48005 942 937 absValue sing_905.htm#SEC981 54595 943 absfact.lib sing_110 5.htm#SEC1181944 absfact_lib sing_110 5.htm#SEC1181945 absolute factorization. sing_110 5.htm#IDX519946 abstract variety, projective space, Grassmannian printVariety sing_2 696.htm#IDX1049947 abstract variety, projective space, Grassmannian sing_2 697.htm#IDX1050948 abstractR sing_144 6.htm#SEC152222284949 actionIsProper sing_167 6.htm#SEC175252474950 addLeftFractions sing_26 56.htm#SEC273238826951 addModules sing_251 1.htm#SEC258751193952 addNvarsTo sing_10 28.htm#SEC110463123938 absfact.lib sing_1107.htm#SEC1183 939 absfact_lib sing_1107.htm#SEC1183 940 absolute factorization. sing_1107.htm#IDX512 941 abstract variety, projective space, Grassmannian printVariety sing_2703.htm#IDX1047 942 abstract variety, projective space, Grassmannian sing_2704.htm#IDX1048 943 abstractR sing_1448.htm#SEC1524 22284 944 actionIsProper sing_1678.htm#SEC1754 52474 945 addLeftFractions sing_2663.htm#SEC2739 38826 946 addModules sing_2518.htm#SEC2594 51193 947 addNvarsTo sing_1030.htm#SEC1106 63123 953 948 addRat sing_801.htm#SEC853 4768 954 addSheaf sing_27 15.htm#SEC279127062955 addcol sing_106 2.htm#SEC113852204956 addcores sing_99 7.htm#SEC107341254957 addnondegeneratevariables addnondegeneratevariables sing_267 2.htm#SEC274840483958 addrow sing_106 3.htm#SEC113947055959 addvarsTo sing_102 7.htm#SEC110317717949 addSheaf sing_2722.htm#SEC2798 27062 950 addcol sing_1064.htm#SEC1140 52204 951 addcores sing_999.htm#SEC1075 41254 952 addnondegeneratevariables addnondegeneratevariables sing_2679.htm#SEC2755 40483 953 addrow sing_1065.htm#SEC1141 47055 954 addvarsTo sing_1029.htm#SEC1105 17717 960 955 ademRelations sing_661.htm#SEC713 30263 961 adjoint sing_108 7.htm#SEC116356619962 adjointIdeal sing_137 5.htm#SEC145111455963 adjunction divisor sing_179 3.htm#IDX793956 adjoint sing_1089.htm#SEC1165 56619 957 adjointIdeal sing_1377.htm#SEC1453 11455 958 adjunction divisor sing_1795.htm#IDX786 964 959 admissibleSub sing_720.htm#SEC772 6583 965 afaces sing_24 16.htm#SEC249228045960 afaces sing_2422.htm#SEC2498 28045 966 961 affine code Fitzgerald-Lax method sing_889.htm#SEC958 967 ainvar.lib sing_167 3.htm#SEC1749968 ainvar_lib sing_167 3.htm#SEC1749969 aksaka.lib sing_18 58.htm#SEC1934970 aksaka_lib sing_18 58.htm#SEC1934971 alexanderpolynomial sing_147 1.htm#SEC154736814972 alexpoly.lib sing_14 68.htm#SEC1544973 alexpoly_lib sing_14 68.htm#SEC1544974 algDependent sing_111 2.htm#SEC118820789975 alg_kernel sing_111 3.htm#SEC1189307976 algebra.lib sing_11 08.htm#SEC1184977 algebra_containment sing_11 09.htm#SEC118547912978 algebra_lib sing_11 08.htm#SEC1184962 ainvar.lib sing_1675.htm#SEC1751 963 ainvar_lib sing_1675.htm#SEC1751 964 aksaka.lib sing_1860.htm#SEC1936 965 aksaka_lib sing_1860.htm#SEC1936 966 alexanderpolynomial sing_1473.htm#SEC1549 36814 967 alexpoly.lib sing_1470.htm#SEC1546 968 alexpoly_lib sing_1470.htm#SEC1546 969 algDependent sing_1114.htm#SEC1190 20789 970 alg_kernel sing_1115.htm#SEC1191 307 971 algebra.lib sing_1110.htm#SEC1186 972 algebra_containment sing_1111.htm#SEC1187 47912 973 algebra_lib sing_1110.htm#SEC1186 979 974 algebraic dependence sing_750.htm#IDX363 980 algebraic field extension sing_132 1.htm#IDX586981 algebraicDependence sing_133 4.htm#SEC141038500975 algebraic field extension sing_1323.htm#IDX579 976 algebraicDependence sing_1336.htm#SEC1412 38500 982 977 algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_880.htm#SEC937 983 978 algorithm of Conti and Traverso sing_876.htm#SEC933 … … 994 989 all_lib sing_898.htm#SEC974 995 990 allowing net access Command line options sing_19.htm#IDX41 996 allprint sing_94 5.htm#SEC10215195997 allreal sing_200 1.htm#SEC207757232998 allrealst sing_ 1999.htm#SEC207540962999 allsquarefree sing_157 5.htm#SEC1651455451000 ambientDimension sing_201 4.htm#SEC209018907991 allprint sing_947.htm#SEC1023 5195 992 allreal sing_2003.htm#SEC2079 57232 993 allrealst sing_2001.htm#SEC2077 40962 994 allsquarefree sing_1577.htm#SEC1653 45545 995 ambientDimension sing_2016.htm#SEC2092 18907 1001 996 and Evaluation of logical expressions sing_101.htm#SEC141 1002 997 and sing_411.htm#SEC451 … … 1014 1009 annihilator of rational function sing_563.htm#IDX343 1015 1010 annihilator of rational function sing_780.htm#IDX388 1016 annil sing_121 6.htm#SEC1292487441011 annil sing_1218.htm#SEC1294 48744 1017 1012 appelF1 sing_582.htm#SEC634 63146 1018 1013 appelF2 sing_583.htm#SEC635 22460 … … 1021 1016 apply sing_378.htm#SEC418 1022 1017 applyAdF sing_532.htm#SEC584 40329 1023 applyPermutationToIntvec applyPermutationToIntvec sing_244 1.htm#SEC2517289001024 arcpoint.lib sing_148 1.htm#SEC15571025 arcpoint_lib sing_148 1.htm#SEC15571026 areEqualLeftFractions areEqualLeftFractions sing_26 58.htm#SEC2734294981027 areZeroElements sing_25 78.htm#SEC2654147281018 applyPermutationToIntvec applyPermutationToIntvec sing_2447.htm#SEC2523 28900 1019 arcpoint.lib sing_1483.htm#SEC1559 1020 arcpoint_lib sing_1483.htm#SEC1559 1021 areEqualLeftFractions areEqualLeftFractions sing_2665.htm#SEC2741 29498 1022 areZeroElements sing_2585.htm#SEC2661 14728 1028 1023 argument, default sing_44.htm#SEC81 1029 1024 argument, optional sing_44.htm#SEC81 1030 arr.lib sing_217 1.htm#SEC22471031 arr2multarr sing_220 4.htm#SEC2280150631032 arrBoolean sing_219 3.htm#SEC2269632561033 arrBoundedChambers sing_221 4.htm#SEC2290183471034 arrBraid sing_219 4.htm#SEC2270340931035 arrCenter sing_218 1.htm#SEC2257245651036 arrCentered sing_218 3.htm#SEC2259159041037 arrCentral sing_218 2.htm#SEC2258140861038 arrCentralize sing_218 4.htm#SEC2260532351039 arrChambers sing_221 3.htm#SEC2289445781040 arrCharPoly sing_221 1.htm#SEC2287441291041 arrCone sing_218 7.htm#SEC2263380681042 arrCoordChange sing_218 5.htm#SEC2261614301043 arrCoordNormalize sing_218 6.htm#SEC2262462731044 arrDecone sing_21 88.htm#SEC2264546371045 arrDer sing_220 1.htm#SEC2277488151046 arrEdelmanReiner sing_2 199.htm#SEC2275590911047 arrEssentialize sing_219 2.htm#SEC226866671048 arrExponents 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sing_2183.htm#SEC2259 24565 1031 arrCentered sing_2185.htm#SEC2261 15904 1032 arrCentral sing_2184.htm#SEC2260 14086 1033 arrCentralize sing_2186.htm#SEC2262 53235 1034 arrChambers sing_2215.htm#SEC2291 44578 1035 arrCharPoly sing_2213.htm#SEC2289 44129 1036 arrCone sing_2189.htm#SEC2265 38068 1037 arrCoordChange sing_2187.htm#SEC2263 61430 1038 arrCoordNormalize sing_2188.htm#SEC2264 46273 1039 arrDecone sing_2190.htm#SEC2266 54637 1040 arrDer sing_2203.htm#SEC2279 48815 1041 arrEdelmanReiner sing_2201.htm#SEC2277 59091 1042 arrEssentialize sing_2194.htm#SEC2270 6667 1043 arrExponents sing_2205.htm#SEC2281 1948 1044 arrFlats sing_2210.htm#SEC2286 64792 1045 arrIsEssential sing_2193.htm#SEC2269 34363 1046 arrIsFree sing_2204.htm#SEC2280 3860 1047 arrLastVar sing_2182.htm#SEC2258 25835 1048 arrLattice sing_2211.htm#SEC2287 58951 1049 arrLocalize sing_2191.htm#SEC2267 56070 1050 arrOrlikSolomon sing_2202.htm#SEC2278 31686 1051 arrPoincare sing_2214.htm#SEC2290 412 1052 arrPrintMatrix sing_2178.htm#SEC2254 21204 1053 arrRandom sing_2199.htm#SEC2275 59986 1054 arrRandomCentral sing_2200.htm#SEC2276 43698 1055 arrRestrict sing_2192.htm#SEC2268 sprintf 1056 arrSet sing_2174.htm#SEC2250 53769 1057 arrSwapVar sing_2181.htm#SEC2257 44919 1058 arrTypeB sing_2197.htm#SEC2273 22358 1059 arrTypeD sing_2198.htm#SEC2274 26495 1060 arr_lib sing_2173.htm#SEC2249 1066 1061 arrange sing_557.htm#SEC609 50350 1067 arrangement sing_217 2.htm#IDX8241068 arrangement sing_217 3.htm#IDX8291069 arrangement sing_220 4.htm#IDX8911070 arrangement sing_220 5.htm#IDX8941071 ask sing_186 6.htm#SEC194238621072 assPrimes sing_112 3.htm#SEC1199sprintf1073 assign sing_217 2.htm#IDX8261062 arrangement sing_2174.htm#IDX817 1063 arrangement sing_2175.htm#IDX822 1064 arrangement sing_2206.htm#IDX884 1065 arrangement sing_2207.htm#IDX887 1066 ask sing_1868.htm#SEC1944 3862 1067 assPrimes sing_1125.htm#SEC1201 sprintf 1068 assign sing_2174.htm#IDX819 1074 1069 assignment,custom Assignments for user defined types sing_187.htm#SEC227 1075 associated tangent FamElemsAtEnvCompPoints sing_940.htm#IDX4 841076 associated tangent sing_941.htm#IDX4 881077 assprimeszerodim.lib assprimeszerodim_lib sing_112 1.htm#SEC11971078 assprimeszerodim_lib assprimeszerodim_lib sing_112 1.htm#SEC11971079 atkins.lib sing_186 7.htm#SEC19431080 atkins_lib sing_186 7.htm#SEC19431070 associated tangent FamElemsAtEnvCompPoints sing_940.htm#IDX474 1071 associated tangent sing_941.htm#IDX478 1072 assprimeszerodim.lib assprimeszerodim_lib sing_1123.htm#SEC1199 1073 assprimeszerodim_lib assprimeszerodim_lib sing_1123.htm#SEC1199 1074 atkins.lib sing_1869.htm#SEC1945 1075 atkins_lib sing_1869.htm#SEC1945 1081 1076 attrib sing_209.htm#SEC249 1082 autGenWeights sing_224 7.htm#SEC2323326421083 autGradAlg sing_224 6.htm#SEC2322211361084 autKS sing_224 5.htm#SEC2321516071085 autX sing_225 0.htm#SEC2326432611086 autXhat sing_22 49.htm#SEC2325359321087 autgradalg.lib sing_224 4.htm#SEC23201088 autgradalg_lib sing_224 4.htm#SEC23201089 automorphism group sing_224 4.htm#IDX9421090 automorphisms sing_224 4.htm#IDX9391091 autonom sing_183 0.htm#SEC1906570441092 autonomDim sing_183 1.htm#SEC1907300551093 awalk1 sing_115 4.htm#SEC1230110441094 awalk2 sing_115 5.htm#SEC123189551077 autGenWeights sing_2249.htm#SEC2325 32642 1078 autGradAlg sing_2248.htm#SEC2324 21136 1079 autKS sing_2247.htm#SEC2323 51607 1080 autX sing_2252.htm#SEC2328 43261 1081 autXhat sing_2251.htm#SEC2327 35932 1082 autgradalg.lib sing_2246.htm#SEC2322 1083 autgradalg_lib sing_2246.htm#SEC2322 1084 automorphism group sing_2246.htm#IDX935 1085 automorphisms sing_2246.htm#IDX932 1086 autonom sing_1832.htm#SEC1908 57044 1087 autonomDim sing_1833.htm#SEC1909 30055 1088 awalk1 sing_1156.htm#SEC1232 11044 1089 awalk2 sing_1157.htm#SEC1233 8955 1095 1090 b-function sing_505.htm#IDX315 1096 1091 bFactor sing_587.htm#SEC639 15179 1097 babyGiant sing_189 6.htm#SEC1972411131098 backward sing_238 1.htm#SEC2457112251092 babyGiant sing_1898.htm#SEC1974 41113 1093 backward sing_2387.htm#SEC2463 11225 1099 1094 bareiss sing_210.htm#SEC250 1100 1095 base2str sing_901.htm#SEC977 sprintf 1101 1096 basering sing_28.htm#IDX76 1102 1097 basering sing_88.htm#SEC128 1103 basicinvariants sing_148 7.htm#SEC1563321361104 belongSemigroup sing_112 6.htm#SEC1202199831105 bernstein sing_153 5.htm#SEC161156051098 basicinvariants sing_1489.htm#SEC1565 32136 1099 belongSemigroup sing_1128.htm#SEC1204 19983 1100 bernstein sing_1537.htm#SEC1613 5605 1106 1101 bernsteinBM sing_545.htm#SEC597 57689 1107 1102 bernsteinLift sing_546.htm#SEC598 22885 1108 bertini sing_135 0.htm#IDX5901109 bertini sing_135 5.htm#IDX5971110 bertini2Singular sing_13 59.htm#SEC1435585011103 bertini sing_1352.htm#IDX583 1104 bertini sing_1357.htm#IDX590 1105 bertini2Singular sing_1361.htm#SEC1437 58501 1111 1106 betti sing_211.htm#SEC251 1112 1107 betti (plural) sing_455.htm#SEC495 1113 betti number sing_2 398.htm#IDX9831108 betti number sing_2404.htm#IDX980 1114 1109 bfct sing_506.htm#SEC558 29858 1115 1110 bfctAnn sing_508.htm#SEC560 36658 … … 1127 1122 bigint operations sing_81.htm#SEC121 1128 1123 bigint related functions bigint related functions sing_82.htm#SEC122 1129 bigintToBinary sing_24 39.htm#SEC2515597421124 bigintToBinary sing_2445.htm#SEC2521 59742 1130 1125 bigintmat sing_83.htm#SEC123 1131 1126 bigintmat declarations bigintmat declarations sing_84.htm#SEC124 … … 1136 1131 bimodules.lib sing_498.htm#SEC550 1137 1132 bimodules_lib sing_498.htm#SEC550 1138 binaryToBigint sing_244 0.htm#SEC2516sprintf1139 binary_add sing_19 19.htm#SEC1995428171133 binaryToBigint sing_2446.htm#SEC2522 sprintf 1134 binary_add sing_1921.htm#SEC1997 42817 1140 1135 binomial sing_906.htm#SEC982 23208 1141 binomials2intmat sing_128 2.htm#SEC1358588041142 birational map, image, inverse. sing_137 6.htm#IDX6221136 binomials2intmat sing_1284.htm#SEC1360 58804 1137 birational map, image, inverse. sing_1378.htm#IDX615 1143 1138 bistd sing_499.htm#SEC551 45237 1144 1139 bisyzygies sing_498.htm#IDX304 … … 1148 1143 block sing_40.htm#SEC70 1149 1144 block sing_377.htm#SEC417 1150 blowUp sing_142 7.htm#SEC1503348191151 blowUp2 sing_14 28.htm#SEC1504652641152 blowUpBO sing_143 4.htm#SEC1510581461153 blowup0 sing_113 1.htm#SEC1207444511154 boolean sing_219 3.htm#IDX8681145 blowUp sing_1429.htm#SEC1505 34819 1146 blowUp2 sing_1430.htm#SEC1506 65264 1147 blowUpBO sing_1436.htm#SEC1512 58146 1148 blowup0 sing_1133.htm#SEC1209 44451 1149 boolean sing_2195.htm#IDX861 1155 1150 boolean expressions sing_100.htm#SEC140 1156 1151 boolean operations sing_101.htm#SEC141 1157 boolean_constant sing_222 7.htm#SEC2303528731158 boolean_ideal sing_223 1.htm#SEC2307535151159 boolean_poly sing_22 28.htm#SEC2304416521160 boolean_poly_ring sing_222 6.htm#SEC2302sprintf1161 boolean_set sing_223 2.htm#SEC2308582351162 boolean_std sing_222 5.htm#SEC230159211163 border basis sing_26 86.htm#IDX10331164 borderBasis sing_26 87.htm#SEC2763331721165 boundBuFou sing_199 6.htm#SEC2072265891166 boundDes sing_ 1998.htm#SEC2074351491167 boundaryLatticePoints boundaryLatticePoints sing_208 4.htm#SEC216062381168 boundposDes sing_199 7.htm#SEC2073588541169 bounds sing_26 74.htm#SEC2750502181170 boxSet sing_26 76.htm#SEC275285521152 boolean_constant sing_2229.htm#SEC2305 52873 1153 boolean_ideal sing_2233.htm#SEC2309 53515 1154 boolean_poly sing_2230.htm#SEC2306 41652 1155 boolean_poly_ring sing_2228.htm#SEC2304 sprintf 1156 boolean_set sing_2234.htm#SEC2310 58235 1157 boolean_std sing_2227.htm#SEC2303 5921 1158 border basis sing_2693.htm#IDX1031 1159 borderBasis sing_2694.htm#SEC2770 33172 1160 boundBuFou sing_1998.htm#SEC2074 26589 1161 boundDes sing_2000.htm#SEC2076 35149 1162 boundaryLatticePoints boundaryLatticePoints sing_2086.htm#SEC2162 6238 1163 boundposDes sing_1999.htm#SEC2075 58854 1164 bounds sing_2681.htm#SEC2757 50218 1165 boxSet sing_2683.htm#SEC2759 8552 1171 1166 bracket sing_358.htm#IDX197 1172 1167 bracket sing_414.htm#SEC454 1173 1168 bracket sing_456.htm#SEC496 1174 braid sing_219 4.htm#IDX8701169 braid sing_2196.htm#IDX863 1175 1170 branchTo procs with different argument types sing_160.htm#SEC200 1176 1171 break sing_379.htm#SEC419 1177 1172 break point sing_393.htm#SEC433 1178 1173 breakpoint sing_380.htm#SEC420 1179 brillnoether.lib sing_225 1.htm#SEC23271180 brillnoether_lib sing_225 1.htm#SEC23271181 brnoeth.lib sing_179 2.htm#SEC18681182 brnoeth_lib sing_179 2.htm#SEC18681174 brillnoether.lib sing_2253.htm#SEC2329 1175 brillnoether_lib sing_2253.htm#SEC2329 1176 brnoeth.lib sing_1794.htm#SEC1870 1177 brnoeth_lib sing_1794.htm#SEC1870 1183 1178 browser, command line option Command line options sing_19.htm#IDX44 1184 1179 browser, setting the sing_358.htm#IDX193 1185 1180 browsers The online help system sing_16.htm#IDX21 1186 1181 browsers, setting the sing_358.htm#IDX192 1187 bubblesort sing_18 69.htm#SEC1945632781188 busadj sing_108 5.htm#SEC1161363011189 bvar sing_22 39.htm#SEC2315527731182 bubblesort sing_1871.htm#SEC1947 63278 1183 busadj sing_1087.htm#SEC1163 36301 1184 bvar sing_2241.htm#SEC2317 52773 1190 1185 c, module ordering sing_862.htm#IDX415 1191 cProj sing_229 3.htm#SEC2369240371192 calculateI sing_140 1.htm#SEC1477311071193 calculate_max_sum sing_19 38.htm#SEC201447061194 calculate_ordering sing_191 6.htm#SEC1992426161186 cProj sing_2295.htm#SEC2371 24037 1187 calculateI sing_1403.htm#SEC1479 31107 1188 calculate_max_sum sing_1940.htm#SEC2016 4706 1189 calculate_ordering sing_1918.htm#SEC1994 42616 1195 1190 cancelunit, option sing_315.htm#IDX171 1196 canonMap sing_11 59.htm#SEC1235475991197 canoncial form sing_928.htm#IDX4 451198 canoncial form sing_929.htm#IDX4 471199 canoncial form sing_930.htm#IDX44 91200 canonical sing_924.htm#IDX4 331201 canonical sing_932.htm#IDX4591202 canonical form sing_933.htm#IDX4641203 canonical form sing_934.htm#IDX4661204 canonicalizeCone sing_201 5.htm#SEC209162511205 canonize sing_18 38.htm#SEC1914540901206 cantoradd sing_195 2.htm#SEC2028553041207 cantormult sing_195 5.htm#SEC2031575691208 cantorred sing_195 3.htm#SEC2029465021209 cardGroup sing_11 28.htm#SEC120455531191 canonMap sing_1161.htm#SEC1237 47599 1192 canoncial form sing_928.htm#IDX436 1193 canoncial form sing_929.htm#IDX438 1194 canoncial form sing_930.htm#IDX440 1195 canonical sing_924.htm#IDX424 1196 canonical form sing_933.htm#IDX454 1197 canonical form sing_934.htm#IDX456 1198 canonical, sing_932.htm#IDX450 1199 canonicalizeCone sing_2017.htm#SEC2093 6251 1200 canonize sing_1840.htm#SEC1916 54090 1201 cantoradd sing_1954.htm#SEC2030 55304 1202 cantormult sing_1957.htm#SEC2033 57569 1203 cantorred sing_1955.htm#SEC2031 46502 1204 cardGroup sing_1130.htm#SEC1206 5553 1210 1205 case No case or switch statement sing_412.htm#SEC452 1211 catNets sing_26 16.htm#SEC2692247601212 cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_274 1.htm#SEC2817553931206 catNets sing_2623.htm#SEC2699 24760 1207 cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_2748.htm#SEC2824 55393 1213 1208 cdd sing_1.htm#IDX10 1214 1209 cddlib sing_1.htm#IDX11 1215 1210 center sing_519.htm#IDX322 65108 1216 1211 center sing_525.htm#SEC577 1217 center sing_218 1.htm#IDX8501218 center sing_218 2.htm#IDX8511219 center sing_218 3.htm#IDX8531220 center sing_218 4.htm#IDX8551212 center sing_2183.htm#IDX843 1213 center sing_2184.htm#IDX844 1214 center sing_2185.htm#IDX846 1215 center sing_2186.htm#IDX848 1221 1216 centerRed sing_524.htm#SEC576 59910 1222 1217 centerVS sing_523.htm#SEC575 27548 1223 central sing_217 5.htm#IDX8361224 central sing_218 2.htm#IDX8521225 central sing_218 4.htm#IDX8541226 central sing_2 198.htm#IDX8791218 central sing_2177.htm#IDX829 1219 central sing_2184.htm#IDX845 1220 central sing_2186.htm#IDX847 1221 central sing_2200.htm#IDX872 1227 1222 central.lib sing_519.htm#SEC571 1228 central1st sing_238 2.htm#SEC2458290901229 central2nd sing_238 3.htm#SEC2459375451223 central1st sing_2388.htm#SEC2464 29090 1224 central2nd sing_2389.htm#SEC2465 37545 1230 1225 central_lib sing_519.htm#SEC571 1231 1226 centralize sing_519.htm#IDX325 … … 1238 1233 cgs sing_900.htm#SEC976 57776 1239 1234 cgsdr sing_925.htm#SEC1001 44460 1240 chAll sing_226 3.htm#SEC233926901241 chAllInv sing_226 4.htm#SEC2340577601242 chDual sing_22 69.htm#SEC2345177451243 chHE sing_226 5.htm#SEC2341639161244 chHom sing_22 78.htm#SEC2354547761245 chNum sing_22 59.htm#SEC2335544151246 chNumbers sing_226 0.htm#SEC2336421341247 chNumbersProj sing_229 7.htm#SEC2373288371248 chProd sing_227 1.htm#SEC2347402091249 chProdE sing_227 2.htm#SEC2348334601250 chProdL sing_227 3.htm#SEC2349447951251 chProdLP sing_227 4.htm#SEC235088811252 chProdM sing_227 5.htm#SEC2351645141253 chProdMP sing_227 6.htm#SEC2352171031254 chProj sing_229 4.htm#SEC2370323111255 chSum sing_226 7.htm#SEC2343210881256 chSymm sing_228 1.htm#SEC2357240661257 chSymm2L sing_228 2.htm#SEC2358516251258 chSymm2LP sing_228 3.htm#SEC2359260991259 chWedge sing_228 4.htm#SEC2360576781260 chWedge2L sing_228 5.htm#SEC2361465971261 chWedge2LP sing_228 6.htm#SEC236288761262 chaincrit sing_196 6.htm#SEC204295021263 chambers sing_221 3.htm#IDX9071264 chambers sing_221 4.htm#IDX9081265 changeDenominator sing_125 4.htm#SEC1330210941266 changechar sing_100 2.htm#SEC1078654541267 changeord sing_100 3.htm#SEC1079551561268 changeordTo sing_102 6.htm#SEC1102419031269 changes sing_27 47.htm#SEC28231270 changevar sing_100 4.htm#SEC1080328291235 chAll sing_2265.htm#SEC2341 2690 1236 chAllInv sing_2266.htm#SEC2342 57760 1237 chDual sing_2271.htm#SEC2347 17745 1238 chHE sing_2267.htm#SEC2343 63916 1239 chHom sing_2280.htm#SEC2356 54776 1240 chNum sing_2261.htm#SEC2337 54415 1241 chNumbers sing_2262.htm#SEC2338 42134 1242 chNumbersProj sing_2299.htm#SEC2375 28837 1243 chProd sing_2273.htm#SEC2349 40209 1244 chProdE sing_2274.htm#SEC2350 33460 1245 chProdL sing_2275.htm#SEC2351 44795 1246 chProdLP sing_2276.htm#SEC2352 8881 1247 chProdM sing_2277.htm#SEC2353 64514 1248 chProdMP sing_2278.htm#SEC2354 17103 1249 chProj sing_2296.htm#SEC2372 32311 1250 chSum sing_2269.htm#SEC2345 21088 1251 chSymm sing_2283.htm#SEC2359 24066 1252 chSymm2L sing_2284.htm#SEC2360 51625 1253 chSymm2LP sing_2285.htm#SEC2361 26099 1254 chWedge sing_2286.htm#SEC2362 57678 1255 chWedge2L sing_2287.htm#SEC2363 46597 1256 chWedge2LP sing_2288.htm#SEC2364 8876 1257 chaincrit sing_1968.htm#SEC2044 9502 1258 chambers sing_2215.htm#IDX900 1259 chambers sing_2216.htm#IDX901 1260 changeDenominator sing_1256.htm#SEC1332 21094 1261 changechar sing_1004.htm#SEC1080 65454 1262 changeord sing_1005.htm#SEC1081 55156 1263 changeordTo sing_1028.htm#SEC1104 41903 1264 changes sing_2754.htm#SEC2830 1265 changevar sing_1006.htm#SEC1082 32829 1271 1266 char sing_212.htm#SEC252 1272 1267 charInfo sing_580.htm#SEC632 11034 1273 1268 charVariety sing_579.htm#SEC631 18306 1274 1269 char_series sing_213.htm#SEC253 1275 characteristic exponents sing_147 5.htm#IDX6461276 characteristic exponents sing_147 6.htm#IDX6511277 characteristic exponents sing_147 7.htm#IDX6541278 characteristic exponents sing_14 78.htm#IDX6581279 characteristic exponents sing_156 2.htm#IDX7641280 characteristic polynomial sing_221 1.htm#IDX9051270 characteristic exponents sing_1477.htm#IDX639 1271 characteristic exponents sing_1478.htm#IDX644 1272 characteristic exponents sing_1479.htm#IDX647 1273 characteristic exponents sing_1480.htm#IDX651 1274 characteristic exponents sing_1564.htm#IDX757 1275 characteristic polynomial sing_2213.htm#IDX898 1281 1276 characteristic variety sing_563.htm#IDX350 1282 1277 characteristic variety sing_780.htm#IDX384 1283 charexp2conductor sing_14 78.htm#SEC1554sprintf1284 charexp2generators sing_147 6.htm#SEC1552168381285 charexp2inter sing_147 7.htm#SEC1553398811286 charexp2multseq sing_147 5.htm#SEC15513341287 charexp2poly sing_14 79.htm#SEC1555sprintf1288 charpoly sing_108 6.htm#SEC1162295611278 charexp2conductor sing_1480.htm#SEC1556 sprintf 1279 charexp2generators sing_1478.htm#SEC1554 16838 1280 charexp2inter sing_1479.htm#SEC1555 39881 1281 charexp2multseq sing_1477.htm#SEC1553 334 1282 charexp2poly sing_1481.htm#SEC1557 sprintf 1283 charpoly sing_1088.htm#SEC1164 29561 1289 1284 charstr sing_214.htm#SEC254 1290 1285 checkFactor sing_556.htm#SEC608 55900 1291 1286 checkRoot sing_551.htm#SEC603 37045 1292 chern sing_22 58.htm#SEC233449161293 chern.lib sing_225 3.htm#SEC23291294 chernCharPoly sing_230 0.htm#SEC2376316101295 chernPoly sing_2 299.htm#SEC2375313161296 chern_lib sing_225 3.htm#SEC23291297 chineseRem sing_188 7.htm#SEC1963385601287 chern sing_2260.htm#SEC2336 4916 1288 chern.lib sing_2255.htm#SEC2331 1289 chernCharPoly sing_2302.htm#SEC2378 31610 1290 chernPoly sing_2301.htm#SEC2377 31316 1291 chern_lib sing_2255.htm#SEC2331 1292 chineseRem sing_1889.htm#SEC1965 38560 1298 1293 chinrem sing_215.htm#SEC255 1299 chinrempoly sing_264 2.htm#SEC2718423121300 chinrestp sing_194 6.htm#SEC2022247791301 cimonom.lib sing_231 5.htm#SEC23911302 cimonom_lib sing_231 5.htm#SEC23911303 cisimplicial.lib sing_112 4.htm#SEC12001304 cisimplicial_lib sing_112 4.htm#SEC12001305 classification sing_23 19.htm#IDX9451306 classify sing_14 88.htm#SEC156449531307 classify.lib sing_148 6.htm#SEC15621308 classify2.lib sing_23 19.htm#SEC23951309 classify2_lib sing_23 19.htm#SEC23951310 classifyCeq sing_150 5.htm#SEC1581427191311 classifyMapGerms.lib classifyMapGerms_lib sing_233 1.htm#SEC24071312 classifyMapGerms_lib classifyMapGerms_lib sing_233 1.htm#SEC24071313 classifySimpleMaps sing_233 7.htm#SEC2413621761314 classifySimpleMaps1 sing_23 38.htm#SEC2414247891315 classifyUnimodalMaps classifyUnimodalMaps sing_23 39.htm#SEC2415634641316 classify_aeq.lib sing_232 2.htm#SEC23981317 classify_aeq_lib sing_232 2.htm#SEC23981318 classify_lib sing_148 6.htm#SEC15621319 classifyceq.lib sing_150 4.htm#IDX6611320 classifyceq_lib sing_150 4.htm#IDX6621321 classifyci.lib sing_150 6.htm#IDX6631322 classifyci_lib sing_150 6.htm#IDX6641323 classifyicis sing_150 7.htm#SEC1583376511324 classpoly sing_2 298.htm#SEC2374457241325 cleanTmp sing_216 2.htm#SEC2238141081326 cleanunit sing_1 399.htm#SEC1475sprintf1294 chinrempoly sing_2649.htm#SEC2725 42312 1295 chinrestp sing_1948.htm#SEC2024 24779 1296 cimonom.lib sing_2317.htm#SEC2393 1297 cimonom_lib sing_2317.htm#SEC2393 1298 cisimplicial.lib sing_1126.htm#SEC1202 1299 cisimplicial_lib sing_1126.htm#SEC1202 1300 classification sing_2321.htm#IDX938 1301 classify sing_1490.htm#SEC1566 4953 1302 classify.lib sing_1488.htm#SEC1564 1303 classify2.lib sing_2321.htm#SEC2397 1304 classify2_lib sing_2321.htm#SEC2397 1305 classifyCeq sing_1507.htm#SEC1583 42719 1306 classifyMapGerms.lib classifyMapGerms_lib sing_2333.htm#SEC2409 1307 classifyMapGerms_lib classifyMapGerms_lib sing_2333.htm#SEC2409 1308 classifySimpleMaps sing_2339.htm#SEC2415 62176 1309 classifySimpleMaps1 sing_2340.htm#SEC2416 24789 1310 classifyUnimodalMaps classifyUnimodalMaps sing_2341.htm#SEC2417 63464 1311 classify_aeq.lib sing_2324.htm#SEC2400 1312 classify_aeq_lib sing_2324.htm#SEC2400 1313 classify_lib sing_1488.htm#SEC1564 1314 classifyceq.lib sing_1506.htm#IDX654 1315 classifyceq_lib sing_1506.htm#IDX655 1316 classifyci.lib sing_1508.htm#IDX656 1317 classifyci_lib sing_1508.htm#IDX657 1318 classifyicis sing_1509.htm#SEC1585 37651 1319 classpoly sing_2300.htm#SEC2376 45724 1320 cleanTmp sing_2164.htm#SEC2240 14108 1321 cleanunit sing_1401.htm#SEC1477 sprintf 1327 1322 cleardenom sing_216.htm#SEC256 1328 1323 close sing_217.htm#SEC257 1329 closed_points sing_180 2.htm#SEC1878472691330 closetex sing_17 69.htm#SEC1845423341331 closureFrac sing_124 7.htm#SEC132392521332 coDim sing_233 3.htm#SEC2409606801333 coDimMap sing_233 2.htm#SEC240820021324 closed_points sing_1804.htm#SEC1880 47269 1325 closetex sing_1771.htm#SEC1847 42334 1326 closureFrac sing_1249.htm#SEC1325 9252 1327 coDim sing_2335.htm#SEC2411 60680 1328 coDimMap sing_2334.htm#SEC2410 2002 1334 1329 coHom sing_773.htm#SEC825 51043 1335 codim sing_160 0.htm#SEC1676142531336 codimension sing_201 6.htm#SEC2092322071330 codim sing_1602.htm#SEC1678 14253 1331 codimension sing_2018.htm#SEC2094 32207 1337 1332 coding theory sing_854.htm#SEC906 1338 1333 coef sing_218.htm#SEC258 1339 coefficient sing_217 4.htm#IDX8321340 coefficient sing_217 5.htm#IDX8351341 coefficient sing_217 6.htm#IDX8391334 coefficient sing_2176.htm#IDX825 1335 coefficient sing_2177.htm#IDX828 1336 coefficient sing_2178.htm#IDX832 1342 1337 coefficient field sing_144.htm#SEC184 1343 1338 coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45 1344 1339 coefficients, long sing_811.htm#SEC863 1345 coeffmod sing_186 4.htm#SEC1940235311340 coeffmod sing_1866.htm#SEC1942 23531 1346 1341 coeffs sing_219.htm#SEC259 1347 coker sing_2507.htm#SEC2583 35639 1348 colength of derivations curveColengthDerivations sing_2344.htm#IDX961 1349 collectDiv sing_1444.htm#SEC1520 50348 1350 colrank sing_1836.htm#SEC1912 52290 1351 colred sing_1069.htm#SEC1145 1693 1342 coker sing_2514.htm#SEC2590 35639 1343 colength of derivations curveColengthDerivations sing_2350.htm#IDX958 1344 collectDiv sing_1446.htm#SEC1522 50348 1345 colrank sing_1838.htm#SEC1914 52290 1346 colred sing_1071.htm#SEC1147 1693 1347 combinat.lib sing_2342.htm#SEC2418 1348 combinat_lib sing_2342.htm#SEC2418 1352 1349 commRing sing_804.htm#SEC856 30892 1353 1350 comma sing_413.htm#SEC453 … … 1359 1356 commands (plural) sing_454.htm#IDX302 1360 1357 comment sing_36.htm#IDX108 1361 compareMatrix sing_25 15.htm#SEC2591499301362 compareModules sing_251 0.htm#SEC258636921363 compareTasks sing_103 3.htm#SEC1109451571364 compareVectors sing_25 35.htm#SEC2611128811365 completeReduction sing_16 78.htm#SEC1754571571358 compareMatrix sing_2522.htm#SEC2598 49930 1359 compareModules sing_2517.htm#SEC2593 3692 1360 compareTasks sing_1035.htm#SEC1111 45157 1361 compareVectors sing_2542.htm#SEC2618 12881 1362 completeReduction sing_1680.htm#SEC1756 57157 1366 1363 complex sing_28.htm#IDX75 1367 complexClassify sing_232 0.htm#SEC2396227961368 complexSingType sing_150 2.htm#SEC1578344831369 complexType sing_232 1.htm#SEC2397557721364 complexClassify sing_2322.htm#SEC2398 22796 1365 complexSingType sing_1504.htm#SEC1580 34483 1366 complexType sing_2323.htm#SEC2399 55772 1370 1367 compregb.lib sing_899.htm#SEC975 1371 1368 compregb_lib sing_899.htm#SEC975 1372 1369 comprehensive Groebner system sing_899.htm#IDX421 1373 compress sing_104 6.htm#SEC1122619981374 computeAfaceOrbits sing_24 26.htm#SEC2502286831375 computeConstant sing_114 4.htm#SEC1220550241376 computeGromovWitten sing_114 7.htm#SEC1223188341377 computeN sing_14 48.htm#SEC1524616281378 computeV sing_144 7.htm#SEC1523403161379 computemcm sing_140 6.htm#SEC1482369561380 concat sing_104 7.htm#SEC1123166531381 conductor sing_125 5.htm#IDX5781382 conductor sing_14 78.htm#IDX6571383 conductor sing_234 2.htm#IDX9551384 conductor, degree sing_156 2.htm#IDX7671370 compress sing_1048.htm#SEC1124 61998 1371 computeAfaceOrbits sing_2432.htm#SEC2508 28683 1372 computeConstant sing_1146.htm#SEC1222 55024 1373 computeGromovWitten sing_1149.htm#SEC1225 18834 1374 computeN sing_1450.htm#SEC1526 61628 1375 computeV sing_1449.htm#SEC1525 40316 1376 computemcm sing_1408.htm#SEC1484 36956 1377 concat sing_1049.htm#SEC1125 16653 1378 conductor sing_1257.htm#IDX571 1379 conductor sing_1480.htm#IDX650 1380 conductor sing_2348.htm#IDX952 1381 conductor, degree sing_1564.htm#IDX760 1385 1382 cone sing_188.htm#SEC228 1386 cone sing_218 7.htm#IDX8591387 cone sing_21 88.htm#IDX8611388 coneLink sing_20 19.htm#SEC2095136351389 coneViaInequalities sing_20 18.htm#SEC2094256611390 coneViaPoints sing_201 7.htm#SEC209333861391 conic, parametrization, rational point. sing_138 3.htm#IDX6271392 conicWithTangents sing_21 38.htm#SEC2214607521393 constructH sing_140 7.htm#SEC1483595771394 constructblwup sing_14 08.htm#SEC1484193261395 constructible set sing_933.htm#IDX4 621396 constructible sets sing_934.htm#IDX4 651397 constructlastblwup sing_14 09.htm#SEC148576391398 constructor sing_220 4.htm#IDX8921399 constructor sing_220 5.htm#IDX8951400 contact matrix sing_147 7.htm#IDX6531401 containedQ sing_175 7.htm#SEC1833467181402 containsAsFace sing_202 0.htm#SEC2096251591403 containsInCollection containsInCollection sing_205 3.htm#SEC2129143681404 containsInSupport sing_202 1.htm#SEC2097324931405 containsPositiveVector containsPositiveVector sing_202 2.htm#SEC2098270421406 containsRelatively sing_202 3.htm#SEC2099171261407 content sing_97 6.htm#SEC105290951383 cone sing_2189.htm#IDX852 1384 cone sing_2190.htm#IDX854 1385 coneLink sing_2021.htm#SEC2097 13635 1386 coneViaInequalities sing_2020.htm#SEC2096 25661 1387 coneViaPoints sing_2019.htm#SEC2095 3386 1388 conic, parametrization, rational point. sing_1385.htm#IDX620 1389 conicWithTangents sing_2140.htm#SEC2216 60752 1390 constructH sing_1409.htm#SEC1485 59577 1391 constructblwup sing_1410.htm#SEC1486 19326 1392 constructible set sing_933.htm#IDX452 1393 constructible sets sing_934.htm#IDX455 1394 constructlastblwup sing_1411.htm#SEC1487 7639 1395 constructor sing_2206.htm#IDX885 1396 constructor sing_2207.htm#IDX888 1397 contact matrix sing_1479.htm#IDX646 1398 containedQ sing_1759.htm#SEC1835 46718 1399 containsAsFace sing_2022.htm#SEC2098 25159 1400 containsInCollection containsInCollection sing_2055.htm#SEC2131 14368 1401 containsInSupport sing_2023.htm#SEC2099 32493 1402 containsPositiveVector containsPositiveVector sing_2024.htm#SEC2100 27042 1403 containsRelatively sing_2025.htm#SEC2101 17126 1404 content sing_978.htm#SEC1054 9095 1408 1405 contentSB, option sing_315.htm#IDX172 1409 1406 continue Behavior of continue sing_381.htm#SEC421 … … 1411 1408 contraHom sing_774.htm#SEC826 54270 1412 1409 contract sing_220.htm#SEC260 1413 contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_272 2.htm#IDX10621414 contributionBundle sing_272 2.htm#SEC2798328741410 contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_2729.htm#IDX1060 1411 contributionBundle sing_2729.htm#SEC2805 32874 1415 1412 contributors sing_358.htm#IDX200 1416 control sing_18 28.htm#SEC1904444981417 control.lib sing_182 7.htm#SEC19031418 controlDim sing_18 29.htm#SEC190524171419 controlExample sing_184 1.htm#SEC191726781420 control_Matrix sing_153 0.htm#SEC1606sprintf1421 control_lib sing_182 7.htm#SEC19031422 convertLeftToRightFraction convertLeftToRightFraction sing_26 55.htm#SEC273143181423 convertRightToLeftFraction convertRightToLeftFraction sing_26 54.htm#SEC2730193891424 convertdata sing_140 4.htm#SEC1480546291425 convexHull sing_202 4.htm#SEC2100566901426 convexIntersection sing_202 5.htm#SEC2101635871413 control sing_1830.htm#SEC1906 44498 1414 control.lib sing_1829.htm#SEC1905 1415 controlDim sing_1831.htm#SEC1907 2417 1416 controlExample sing_1843.htm#SEC1919 2678 1417 control_Matrix sing_1532.htm#SEC1608 sprintf 1418 control_lib sing_1829.htm#SEC1905 1419 convertLeftToRightFraction convertLeftToRightFraction sing_2662.htm#SEC2738 4318 1420 convertRightToLeftFraction convertRightToLeftFraction sing_2661.htm#SEC2737 19389 1421 convertdata sing_1406.htm#SEC1482 54629 1422 convexHull sing_2026.htm#SEC2102 56690 1423 convexIntersection sing_2027.htm#SEC2103 63587 1427 1424 convloc sing_560.htm#SEC612 19122 1428 coordinate change sing_218 4.htm#IDX8561429 coordinate change sing_218 5.htm#IDX8571430 coordinate change sing_218 6.htm#IDX8581431 coordinates sing_198 4.htm#IDX8091432 coords sing_198 4.htm#SEC2060293621433 copyTask sing_103 2.htm#SEC1108653311425 coordinate change sing_2186.htm#IDX849 1426 coordinate change sing_2187.htm#IDX850 1427 coordinate change sing_2188.htm#IDX851 1428 coordinates sing_1986.htm#IDX802 1429 coords sing_1986.htm#SEC2062 29362 1430 copyTask sing_1034.htm#SEC1110 65331 1434 1431 copyright sing_1.htm#IDX1 1435 corank sing_14 89.htm#SEC1565337091436 cornerMonomials sing_128 5.htm#SEC1361339951437 countPoints sing_19 09.htm#SEC1985585661438 coverings sing_114 6.htm#IDX5371439 coverings sing_114 7.htm#IDX5411432 corank sing_1491.htm#SEC1567 33709 1433 cornerMonomials sing_1287.htm#SEC1363 33995 1434 countPoints sing_1911.htm#SEC1987 58566 1435 coverings sing_1148.htm#IDX530 1436 coverings sing_1149.htm#IDX534 1440 1437 cpu sing_358.htm#IDX202 1441 1438 cpu sing_358.htm#IDX275 1442 createBO sing_143 5.htm#SEC1511326691443 createGradedRingHomomorphism createGradedRingHomomorphism sing_25 54.htm#SEC2630621771444 createGroup sing_25 47.htm#SEC2623285001445 createQuotientGroup sing_25 48.htm#SEC2624263741446 createTask sing_103 0.htm#SEC1106484041447 createTorsionFreeGroup createTorsionFreeGroup sing_25 49.htm#SEC2625519441448 createlist sing_141 7.htm#SEC1493617811439 createBO sing_1437.htm#SEC1513 32669 1440 createGradedRingHomomorphism createGradedRingHomomorphism sing_2561.htm#SEC2637 62177 1441 createGroup sing_2554.htm#SEC2630 28500 1442 createQuotientGroup sing_2555.htm#SEC2631 26374 1443 createTask sing_1032.htm#SEC1108 48404 1444 createTorsionFreeGroup createTorsionFreeGroup sing_2556.htm#SEC2632 51944 1445 createlist sing_1419.htm#SEC1495 61781 1449 1446 cring sing_73.htm#SEC113 1450 1447 cring declarations sing_74.htm#SEC114 … … 1453 1450 cring related functions cring related functions sing_77.htm#SEC117 1454 1451 crossprod sing_221.htm#SEC261 1455 crypto.lib sing_188 2.htm#SEC19581456 crypto_lib sing_188 2.htm#SEC19581457 cup sing_116 0.htm#SEC1236579721458 cupproduct sing_116 1.htm#SEC1237433491459 curve singularities sing_14 68.htm#IDX6401460 curve singularities sing_155 6.htm#IDX7621461 curve singularity sing_234 0.htm#IDX9501462 curveColengthDerivations curveColengthDerivations sing_23 44.htm#SEC242020781463 curveConductorMult sing_234 2.htm#SEC2418158971464 curveDeligneNumber sing_234 3.htm#SEC2419122941465 curveDeltaInv sing_234 1.htm#SEC2417163751466 curveInv.lib sing_234 0.htm#SEC24161467 curveInv_lib sing_234 0.htm#SEC24161468 curvepar.lib sing_15 09.htm#SEC15851469 curvepar_lib sing_15 09.htm#SEC15851452 crypto.lib sing_1884.htm#SEC1960 1453 crypto_lib sing_1884.htm#SEC1960 1454 cup sing_1162.htm#SEC1238 57972 1455 cupproduct sing_1163.htm#SEC1239 43349 1456 curve singularities sing_1470.htm#IDX633 1457 curve singularities sing_1558.htm#IDX755 1458 curve singularity sing_2346.htm#IDX947 1459 curveColengthDerivations curveColengthDerivations sing_2350.htm#SEC2426 2078 1460 curveConductorMult sing_2348.htm#SEC2424 15897 1461 curveDeligneNumber sing_2349.htm#SEC2425 12294 1462 curveDeltaInv sing_2347.htm#SEC2423 16375 1463 curveInv.lib sing_2346.htm#SEC2422 1464 curveInv_lib sing_2346.htm#SEC2422 1465 curvepar.lib sing_1511.htm#SEC1587 1466 curvepar_lib sing_1511.htm#SEC1587 1470 1467 custom assignment Assignments for user defined types sing_187.htm#SEC227 1471 1468 custom command Commands for user defined types sing_186.htm#SEC226 1472 1469 custom type Definition of a user defined type sing_183.htm#SEC223 1473 customstd.lib sing_221 6.htm#SEC22921474 customstd_lib sing_221 6.htm#SEC22921475 cycleLength sing_207 5.htm#SEC2151168981476 cyclePoints sing_20 79.htm#SEC2155544601477 cyclic sing_96 3.htm#SEC1039213751470 customstd.lib sing_2218.htm#SEC2294 1471 customstd_lib sing_2218.htm#SEC2294 1472 cycleLength sing_2077.htm#SEC2153 16898 1473 cyclePoints sing_2081.htm#SEC2157 54460 1474 cyclic sing_965.htm#SEC1041 21375 1478 1475 cyclic code Codes and the decoding problem sing_886.htm#SEC945 1479 cyclotomic sing_164 3.htm#SEC1719337491476 cyclotomic sing_1645.htm#SEC1721 33749 1480 1477 datetime sing_222.htm#SEC262 50127 1481 1478 dbprint sing_223.htm#SEC263 1482 deRham.lib sing_23 45.htm#SEC24211479 deRham.lib sing_2351.htm#SEC2427 1483 1480 deRhamCohom sing_577.htm#SEC629 58222 1484 1481 deRhamCohomIdeal sing_578.htm#SEC630 42169 1485 deRhamCohomology sing_23 46.htm#SEC2422419471486 deRham_lib sing_23 45.htm#SEC24211482 deRhamCohomology sing_2352.htm#SEC2428 41947 1483 deRham_lib sing_2351.htm#SEC2427 1487 1484 debugLib, option sing_315.htm#IDX176 1488 debug_log sing_1 499.htm#SEC1575620431485 debug_log sing_1501.htm#SEC1577 62043 1489 1486 debugger Source code debugger sing_66.htm#SEC103 1490 1487 debugging library code Source code debugger sing_66.htm#SEC103 1491 dec1var sing_121 5.htm#SEC1291360981492 decimal sing_188 3.htm#SEC1959560661493 decode sing_18 19.htm#SEC1895643301494 decodeCode sing_182 1.htm#SEC1897282621495 decodeRandom sing_182 0.htm#SEC1896401181496 decodeRandomFL sing_182 4.htm#SEC1900354231497 decodeSV sing_180 1.htm#SEC1877379751498 decodegb.lib sing_180 6.htm#SEC18821499 decodegb_lib sing_180 6.htm#SEC18821488 dec1var sing_1217.htm#SEC1293 36098 1489 decimal sing_1885.htm#SEC1961 56066 1490 decode sing_1821.htm#SEC1897 64330 1491 decodeCode sing_1823.htm#SEC1899 28262 1492 decodeRandom sing_1822.htm#SEC1898 40118 1493 decodeRandomFL sing_1826.htm#SEC1902 35423 1494 decodeSV sing_1803.htm#SEC1879 37975 1495 decodegb.lib sing_1808.htm#SEC1884 1496 decodegb_lib sing_1808.htm#SEC1884 1500 1497 decoding, decoding problem Codes and the decoding problem sing_886.htm#SEC946 1501 decoef sing_18 49.htm#SEC1925602841502 decomposition of modules sing_12 08.htm#IDX5661503 decomposition, numerical sing_135 5.htm#IDX5951504 decone sing_218 7.htm#IDX8601505 decone sing_21 88.htm#IDX8621498 decoef sing_1851.htm#SEC1927 60284 1499 decomposition of modules sing_1210.htm#IDX559 1500 decomposition, numerical sing_1357.htm#IDX588 1501 decone sing_2189.htm#IDX853 1502 decone sing_2190.htm#IDX855 1506 1503 def sing_88.htm#SEC128 1507 1504 def declarations sing_89.htm#SEC129 1508 1505 defRes, option sing_315.htm#IDX177 1509 1506 default argument sing_44.htm#SEC81 1510 defineHomogeneous sing_25 87.htm#SEC2663550721507 defineHomogeneous sing_2594.htm#SEC2670 55072 1511 1508 defined sing_224.htm#SEC264 1512 defl sing_136 6.htm#SEC1442118251513 deform sing_160 1.htm#SEC167752501514 deform.lib sing_152 0.htm#SEC15961515 deform_lib sing_152 0.htm#SEC15961516 defring sing_100 5.htm#SEC108118141517 defringp sing_100 7.htm#SEC1083429051518 defrings sing_100 6.htm#SEC108210341509 defl sing_1368.htm#SEC1444 11825 1510 deform sing_1603.htm#SEC1679 5250 1511 deform.lib sing_1522.htm#SEC1598 1512 deform_lib sing_1522.htm#SEC1598 1513 defring sing_1007.htm#SEC1083 1814 1514 defringp sing_1009.htm#SEC1085 42905 1515 defrings sing_1008.htm#SEC1084 1034 1519 1516 deg sing_225.htm#SEC265 1520 1517 degBound sing_395.htm#SEC435 … … 1524 1521 degree of a polynomial Miscellaneous oddities sing_418.htm#IDX296 1525 1522 degree reverse lexicographical ordering sing_860.htm#IDX393 1526 degreeDivisor sing_23 56.htm#SEC2432317511527 degreeFormalDivisor sing_23 64.htm#SEC2440425031528 degreepart sing_17 09.htm#SEC1785530361523 degreeDivisor sing_2362.htm#SEC2438 31751 1524 degreeFormalDivisor sing_2370.htm#SEC2446 42503 1525 degreepart sing_1711.htm#SEC1787 53036 1529 1526 delete sing_126.htm#SEC166 1530 1527 delete sing_227.htm#SEC267 … … 1532 1529 deleteGenerator sing_592.htm#SEC644 24917 1533 1530 deleteSublist sing_907.htm#SEC983 20406 1534 deligne number curveColengthDerivations sing_234 0.htm#IDX9521535 deligne number sing_234 3.htm#IDX9571536 deligne number sing_23 44.htm#IDX9591537 delta sing_15 68.htm#SEC1644569521538 delta invariant sing_12 49.htm#IDX5761539 delta invariant sing_15 68.htm#IDX7721540 delta invariant sing_234 1.htm#IDX9531541 delta invariant. sing_124 1.htm#IDX5691542 delta invariant. sing_124 2.htm#IDX5721543 delta invariant. sing_124 3.htm#IDX5751544 deltaLoc sing_12 49.htm#SEC1325351921531 deligne number curveColengthDerivations sing_2346.htm#IDX949 1532 deligne number sing_2349.htm#IDX954 1533 deligne number sing_2350.htm#IDX956 1534 delta sing_1570.htm#SEC1646 56952 1535 delta invariant sing_1251.htm#IDX569 1536 delta invariant sing_1570.htm#IDX765 1537 delta invariant sing_2347.htm#IDX950 1538 delta invariant. sing_1243.htm#IDX562 1539 delta invariant. sing_1244.htm#IDX565 1540 delta invariant. sing_1245.htm#IDX568 1541 deltaLoc sing_1251.htm#SEC1327 35192 1545 1542 denom_list sing_358.htm#IDX204 1546 1543 denominator sing_228.htm#SEC268 1547 depth sing_116 2.htm#SEC1238177771548 depthIdeal sing_122 5.htm#SEC1301547821549 derivate sing_167 5.htm#SEC1751154091550 derivation sing_220 1.htm#IDX8831551 desingularization sing_24 45.htm#IDX988590411552 desingularization sing_24 46.htm#SEC25221544 depth sing_1164.htm#SEC1240 17777 1545 depthIdeal sing_1227.htm#SEC1303 54782 1546 derivate sing_1677.htm#SEC1753 15409 1547 derivation sing_2203.htm#IDX876 1548 desingularization sing_2451.htm#IDX985 59041 1549 desingularization sing_2452.htm#SEC2528 1553 1550 det sing_229.htm#SEC269 1554 det_B sing_10 88.htm#SEC1164601431555 detadj sing_158 4.htm#SEC166059141556 determinacy sing_267 1.htm#SEC2747448181557 determinecenter sing_13 89.htm#SEC1465444961558 detropicalise sing_215 6.htm#SEC2232380251559 develop sing_15 58.htm#SEC1634484571560 diag sing_10 48.htm#SEC1124567591561 diagInvariants sing_126 4.htm#SEC1340620961562 diag_test sing_108 4.htm#SEC1160314691551 det_B sing_1090.htm#SEC1166 60143 1552 detadj sing_1586.htm#SEC1662 5914 1553 determinacy sing_2678.htm#SEC2754 44818 1554 determinecenter sing_1391.htm#SEC1467 44496 1555 detropicalise sing_2158.htm#SEC2234 38025 1556 develop sing_1560.htm#SEC1636 48457 1557 diag sing_1050.htm#SEC1126 56759 1558 diagInvariants sing_1266.htm#SEC1342 62096 1559 diag_test sing_1086.htm#SEC1162 31469 1563 1560 diff sing_230.htm#SEC270 1564 1561 diffRat sing_803.htm#SEC855 36134 1565 difpoly2tex sing_185 0.htm#SEC192664511562 difpoly2tex sing_1852.htm#SEC1928 6451 1566 1563 dim sing_231.htm#SEC271 1567 1564 dim (plural) sing_457.htm#SEC497 1568 dimGradedPart sing_145 7.htm#SEC1533112621569 dimH sing_145 6.htm#SEC1532385341570 dimMon sing_120 5.htm#SEC1281399711571 dimStack sing_272 0.htm#SEC2796477721572 dim_slocus sing_160 2.htm#SEC1678472181573 dimension sing_202 6.htm#SEC2102352621574 dimension, moduli space of stable maps, rational curves dimStack sing_272 0.htm#IDX10601575 dimensionOfLocalization dimensionOfLocalization sing_24 09.htm#SEC2485256321576 direct_boolean_poly sing_22 29.htm#SEC2305498931577 direct_from_boolean_poly direct_from_boolean_poly sing_223 5.htm#SEC2311369411578 disc sing_187 0.htm#SEC1946452791579 discr sing_162 4.htm#SEC170096421580 discrepancy sing_144 2.htm#SEC151855971565 dimGradedPart sing_1459.htm#SEC1535 11262 1566 dimH sing_1458.htm#SEC1534 38534 1567 dimMon sing_1207.htm#SEC1283 39971 1568 dimStack sing_2727.htm#SEC2803 47772 1569 dim_slocus sing_1604.htm#SEC1680 47218 1570 dimension sing_2028.htm#SEC2104 35262 1571 dimension, moduli space of stable maps, rational curves dimStack sing_2727.htm#IDX1058 1572 dimensionOfLocalization dimensionOfLocalization sing_2415.htm#SEC2491 25632 1573 direct_boolean_poly sing_2231.htm#SEC2307 49893 1574 direct_from_boolean_poly direct_from_boolean_poly sing_2237.htm#SEC2313 36941 1575 disc sing_1872.htm#SEC1948 45279 1576 discr sing_1626.htm#SEC1702 9642 1577 discrepancy sing_1444.htm#SEC1520 5597 1581 1578 discrim sing_942.htm#SEC1018 44091 1582 discussion of parametric ideal sing_924.htm#IDX434 1583 discussion of parametric ideal sing_932.htm#IDX460 1584 disjoint sing_925.htm#IDX436 1585 disp_zdd sing_2242.htm#SEC2318 41439 1586 displayCohom sing_1458.htm#SEC1534 22633 1587 displayHNE sing_1561.htm#SEC1637 29845 1588 displayInvariants sing_1563.htm#SEC1639 13678 1589 displayMultsequence sing_1565.htm#SEC1641 16668 1590 displayPuiseuxExpansion displayPuiseuxExpansion sing_2131.htm#SEC2207 560 1591 displayTropicalLifting displayTropicalLifting sing_2129.htm#SEC2205 28144 1592 distributed computing sing_956.htm#IDX499 1593 distributed computing sing_996.htm#IDX501 1594 distributed computing sing_1029.htm#IDX511 1579 discussion of parametric ideal sing_924.htm#IDX425 1580 disjoint sing_925.htm#IDX427 1581 disp_zdd sing_2244.htm#SEC2320 41439 1582 displayCohom sing_1460.htm#SEC1536 22633 1583 displayHNE sing_1563.htm#SEC1639 29845 1584 displayInvariants sing_1565.htm#SEC1641 13678 1585 displayMultsequence sing_1567.htm#SEC1643 16668 1586 displayPuiseuxExpansion displayPuiseuxExpansion sing_2133.htm#SEC2209 560 1587 displayTropicalLifting displayTropicalLifting sing_2131.htm#SEC2207 28144 1588 distributed computing sing_958.htm#IDX492 1589 distributed computing sing_998.htm#IDX494 1590 distributed computing sing_1031.htm#IDX504 1595 1591 div Miscellaneous oddities sing_81.htm#SEC121 1596 1592 div sing_98.htm#SEC138 1597 1593 div sing_155.htm#SEC195 1598 1594 div sing_418.htm#IDX289 1599 divideUnits sing_184 6.htm#SEC1922267111600 dividelist sing_141 6.htm#SEC1492342101595 divideUnits sing_1848.htm#SEC1924 26711 1596 dividelist sing_1418.htm#SEC1494 34210 1601 1597 division sing_232.htm#SEC272 1602 division sing_926.htm#IDX43 91603 division sing_927.htm#IDX4 411598 division sing_926.htm#IDX430 1599 division sing_927.htm#IDX432 1604 1600 division (plural) sing_458.htm#SEC498 1605 divisor sing_19 49.htm#SEC2025472311606 divisorplus sing_235 0.htm#SEC2426342481607 divisors negativeformaldivisor sing_23 49.htm#IDX9621608 divisors sing_235 0.htm#IDX9631609 divisors sing_235 1.htm#IDX9641610 divisors sing_235 2.htm#IDX9651611 divisors sing_235 3.htm#IDX9661612 divisors sing_23 54.htm#IDX9671613 divisors sing_23 55.htm#IDX9681614 divisors sing_23 56.htm#IDX9691615 divisors sing_23 57.htm#IDX9701616 divisors sing_23 58.htm#IDX9711617 divisors sing_23 59.htm#IDX9721618 divisors sing_236 0.htm#IDX9731619 divisors sing_236 1.htm#IDX9741620 divisors sing_236 2.htm#IDX9751621 divisors sing_236 3.htm#IDX9761622 divisors sing_23 64.htm#IDX9771623 divisors, polyhedra sing_23 65.htm#IDX9781624 divisors, polyhedra sing_23 66.htm#IDX9791625 divisors, polyhedra sing_23 67.htm#IDX9801626 divisors.lib sing_23 48.htm#SEC24241627 divisors_lib sing_23 48.htm#SEC24241601 divisor sing_1951.htm#SEC2027 47231 1602 divisorplus sing_2356.htm#SEC2432 34248 1603 divisors negativeformaldivisor sing_2355.htm#IDX959 1604 divisors sing_2356.htm#IDX960 1605 divisors sing_2357.htm#IDX961 1606 divisors sing_2358.htm#IDX962 1607 divisors sing_2359.htm#IDX963 1608 divisors sing_2360.htm#IDX964 1609 divisors sing_2361.htm#IDX965 1610 divisors sing_2362.htm#IDX966 1611 divisors sing_2363.htm#IDX967 1612 divisors sing_2364.htm#IDX968 1613 divisors sing_2365.htm#IDX969 1614 divisors sing_2366.htm#IDX970 1615 divisors sing_2367.htm#IDX971 1616 divisors sing_2368.htm#IDX972 1617 divisors sing_2369.htm#IDX973 1618 divisors sing_2370.htm#IDX974 1619 divisors, polyhedra sing_2371.htm#IDX975 1620 divisors, polyhedra sing_2372.htm#IDX976 1621 divisors, polyhedra sing_2373.htm#IDX977 1622 divisors.lib sing_2354.htm#SEC2430 1623 divisors_lib sing_2354.htm#SEC2430 1628 1624 dmod.lib sing_540.htm#SEC592 1629 1625 dmodAction sing_798.htm#SEC850 9763 … … 1638 1634 dmodvar.lib sing_596.htm#SEC648 1639 1635 dmodvar_lib sing_596.htm#SEC648 1640 double sing_195 4.htm#SEC2030346971636 double sing_1956.htm#SEC2032 34697 1641 1637 doubleExt sing_766.htm#SEC818 56896 1642 downloading Download instructions sing_27 55.htm#SEC28441638 downloading Download instructions sing_2762.htm#SEC2851 1643 1639 dp, global ordering sing_860.htm#IDX394 1644 drawNewtonSubdivision drawNewtonSubdivision sing_213 4.htm#SEC2210509041645 drawTropicalCurve sing_213 3.htm#SEC2209104411640 drawNewtonSubdivision drawNewtonSubdivision sing_2136.htm#SEC2212 50904 1641 drawTropicalCurve sing_2135.htm#SEC2211 10441 1646 1642 ds, local ordering sing_861.htm#IDX404 1647 dsum sing_10 49.htm#SEC112513031648 dualCone sing_202 7.htm#SEC2103614601649 dualConic sing_21 58.htm#SEC2234310801650 dualPart sing_230 6.htm#SEC2382132791651 dualPartition sing_27 33.htm#SEC2809247391652 dualPolytope sing_206 6.htm#SEC2142320811653 dualSheaf sing_271 1.htm#SEC27876331654 dual_code sing_180 3.htm#SEC1879572291643 dsum sing_1051.htm#SEC1127 1303 1644 dualCone sing_2029.htm#SEC2105 61460 1645 dualConic sing_2160.htm#SEC2236 31080 1646 dualPart sing_2308.htm#SEC2384 13279 1647 dualPartition sing_2740.htm#SEC2816 24739 1648 dualPolytope sing_2068.htm#SEC2144 32081 1649 dualSheaf sing_2718.htm#SEC2794 633 1650 dual_code sing_1805.htm#SEC1881 57229 1655 1651 dump sing_233.htm#SEC273 1656 dynamic geometry sing_935.htm#IDX4 691657 dynamic geometry sing_936.htm#IDX4 721658 ecart sing_195 7.htm#SEC2033324751652 dynamic geometry sing_935.htm#IDX459 1653 dynamic geometry sing_936.htm#IDX462 1654 ecart sing_1959.htm#SEC2035 32475 1659 1655 echo sing_396.htm#SEC436 1660 eexgcdN sing_188 4.htm#SEC1960532371661 effective sing_23 58.htm#SEC2434530281662 egcdMain sing_175 0.htm#SEC1826253591663 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_208 5.htm#SEC2161382711664 ehrhartRing sing_126 0.htm#SEC1336169661665 eigenvals sing_109 6.htm#SEC1172112281656 eexgcdN sing_1886.htm#SEC1962 53237 1657 effective sing_2364.htm#SEC2440 53028 1658 egcdMain sing_1752.htm#SEC1828 25359 1659 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2087.htm#SEC2163 38271 1660 ehrhartRing sing_1262.htm#SEC1338 16966 1661 eigenvals sing_1098.htm#SEC1174 11228 1666 1662 eigenvalue sing_328.htm#SEC368 1667 eigenvalue sing_109 6.htm#IDX5171668 eigenvalues sing_134 3.htm#SEC141921821669 elemSymmId sing_96 4.htm#SEC1040sprintf1670 elim sing_113 3.htm#SEC1209625851671 elim.lib sing_113 0.htm#SEC12061672 elim1 sing_113 4.htm#SEC1210156531673 elim2 sing_113 5.htm#SEC1211447491674 elimRing sing_113 2.htm#SEC1208121941663 eigenvalue sing_1098.htm#IDX510 1664 eigenvalues sing_1345.htm#SEC1421 2182 1665 elemSymmId sing_966.htm#SEC1042 sprintf 1666 elim sing_1135.htm#SEC1211 62585 1667 elim.lib sing_1132.htm#SEC1208 1668 elim1 sing_1136.htm#SEC1212 15653 1669 elim2 sing_1137.htm#SEC1213 44749 1670 elimRing sing_1134.htm#SEC1210 12194 1675 1671 elimWeight sing_723.htm#SEC775 54297 1676 elim_lib sing_113 0.htm#SEC12061672 elim_lib sing_1132.htm#SEC1208 1677 1673 eliminate sing_234.htm#SEC274 1678 1674 eliminate (plural) sing_459.htm#SEC499 1679 1675 eliminateNC sing_718.htm#SEC770 3777 1680 1676 elimination sing_717.htm#IDX362 1681 elimlinearpart sing_171 0.htm#SEC1786142511682 elimpart sing_171 1.htm#SEC1787102581683 elimpartanyr sing_171 2.htm#SEC1788397511684 elimrep sing_139 7.htm#SEC1473236411685 elliptic curve sing_114 3.htm#IDX5331686 elliptic curves sing_114 0.htm#IDX5271687 elliptic curves sing_114 6.htm#IDX5361688 elliptic curves sing_114 7.htm#IDX5401689 ellipticAdd sing_190 5.htm#SEC1981132791690 ellipticAllPoints sing_191 0.htm#SEC1986607701691 ellipticMult sing_190 6.htm#SEC198215581692 ellipticNF sing_208 2.htm#SEC215850451693 ellipticNFDB sing_208 3.htm#SEC2159279171694 ellipticRandomCurve sing_190 7.htm#SEC1983369801695 ellipticRandomPoint sing_19 08.htm#SEC198468661696 ellipticcovers.lib sing_114 0.htm#IDX5211697 ellipticcovers_lib sing_114 0.htm#IDX5221677 elimlinearpart sing_1712.htm#SEC1788 14251 1678 elimpart sing_1713.htm#SEC1789 10258 1679 elimpartanyr sing_1714.htm#SEC1790 39751 1680 elimrep sing_1399.htm#SEC1475 23641 1681 elliptic curve sing_1145.htm#IDX526 1682 elliptic curves sing_1142.htm#IDX520 1683 elliptic curves sing_1148.htm#IDX529 1684 elliptic curves sing_1149.htm#IDX533 1685 ellipticAdd sing_1907.htm#SEC1983 13279 1686 ellipticAllPoints sing_1912.htm#SEC1988 60770 1687 ellipticMult sing_1908.htm#SEC1984 1558 1688 ellipticNF sing_2084.htm#SEC2160 5045 1689 ellipticNFDB sing_2085.htm#SEC2161 27917 1690 ellipticRandomCurve sing_1909.htm#SEC1985 36980 1691 ellipticRandomPoint sing_1910.htm#SEC1986 6866 1692 ellipticcovers.lib sing_1142.htm#IDX514 1693 ellipticcovers_lib sing_1142.htm#IDX515 1698 1694 else sing_386.htm#SEC426 1699 1695 embedMat sing_749.htm#SEC801 17119 1700 emptyFan sing_205 4.htm#SEC213073961701 encode sing_181 1.htm#SEC1887566871702 endomorphism filtration sing_154 2.htm#IDX7381703 endvfilt sing_154 2.htm#SEC1618266701696 emptyFan sing_2056.htm#SEC2132 7396 1697 encode sing_1813.htm#SEC1889 56687 1698 endomorphism filtration sing_1544.htm#IDX731 1699 endvfilt sing_1544.htm#SEC1620 26670 1704 1700 engine sing_593.htm#SEC645 30876 1705 ensureLeftNcfrac sing_26 04.htm#SEC2680645711706 ensureRightNcfrac sing_26 05.htm#SEC2681141071701 ensureLeftNcfrac sing_2611.htm#SEC2687 64571 1702 ensureRightNcfrac sing_2612.htm#SEC2688 14107 1707 1703 envelop FamElemsAtEnvCompPoints sing_937.htm#SEC1013 27362 1708 envelop sing_937.htm#IDX4 751709 envelop sing_938.htm#IDX4 781710 envelop sing_940.htm#IDX4 831711 envelop sing_941.htm#IDX4 871704 envelop sing_937.htm#IDX465 1705 envelop sing_938.htm#IDX468 1706 envelop sing_940.htm#IDX473 1707 envelop sing_941.htm#IDX477 1712 1708 envelope sing_460.htm#SEC500 1713 1709 enveloping algebra sing_358.htm#IDX208 1714 1710 enveloping algebra sing_498.htm#IDX306 1715 1711 environment variable, DISPLAY The online help system sing_16.htm#IDX29 1716 equalJinI sing_148 5.htm#SEC1561185021717 equalMultiDeg sing_258 0.htm#SEC2656370901718 equations sing_20 28.htm#SEC210478961719 equiRadical sing_130 1.htm#SEC137788841720 equidim sing_130 3.htm#SEC1379385411721 equidimMax sing_130 4.htm#SEC1380492891722 equidimMaxEHV sing_130 5.htm#SEC1381426501723 equidimZ sing_131 6.htm#SEC1392496101724 equising.lib sing_152 5.htm#SEC16011725 equising_lib sing_152 5.htm#SEC16011726 equisingular Tjurina number sing_14 68.htm#IDX6451727 equisingularity ideal sing_152 7.htm#IDX6651728 equisingularity stratum sing_15 28.htm#IDX6661712 equalJinI sing_1487.htm#SEC1563 18502 1713 equalMultiDeg sing_2587.htm#SEC2663 37090 1714 equations sing_2030.htm#SEC2106 7896 1715 equiRadical sing_1303.htm#SEC1379 8884 1716 equidim sing_1305.htm#SEC1381 38541 1717 equidimMax sing_1306.htm#SEC1382 49289 1718 equidimMaxEHV sing_1307.htm#SEC1383 42650 1719 equidimZ sing_1318.htm#SEC1394 49610 1720 equising.lib sing_1527.htm#SEC1603 1721 equising_lib sing_1527.htm#SEC1603 1722 equisingular Tjurina number sing_1470.htm#IDX638 1723 equisingularity ideal sing_1529.htm#IDX658 1724 equisingularity stratum sing_1530.htm#IDX659 1729 1725 error recovery sing_15.htm#SEC21 1730 errorInsert sing_181 4.htm#SEC1890594701731 errorRand sing_181 5.htm#SEC189157271732 errormap sing_23 88.htm#SEC246477821733 esIdeal sing_152 7.htm#SEC1603604771734 esStratum sing_15 28.htm#SEC1604500941735 essential sing_219 1.htm#IDX8651736 essential sing_219 2.htm#IDX8661737 eta sing_207 7.htm#SEC2153607291738 euler sing_186 3.htm#SEC1939105191739 eulerChProj sing_229 6.htm#SEC2372285491726 errorInsert sing_1816.htm#SEC1892 59470 1727 errorRand sing_1817.htm#SEC1893 5727 1728 errormap sing_2394.htm#SEC2470 7782 1729 esIdeal sing_1529.htm#SEC1605 60477 1730 esStratum sing_1530.htm#SEC1606 50094 1731 essential sing_2193.htm#IDX858 1732 essential sing_2194.htm#IDX859 1733 eta sing_2079.htm#SEC2155 60729 1734 euler sing_1865.htm#SEC1941 10519 1735 eulerChProj sing_2298.htm#SEC2374 28549 1740 1736 eval sing_235.htm#SEC275 1741 evalJacobianAtBox sing_268 2.htm#SEC2758427161742 evalPolyAtBox sing_268 1.htm#SEC2757430401743 evaluateFormalDivisor evaluateFormalDivisor sing_236 0.htm#SEC243635351744 evaluatePDivisor sing_23 66.htm#SEC2442188551745 evaluateProduct sing_24 36.htm#SEC2512545151746 evaluate_reynolds sing_16 48.htm#SEC1724463531747 evalutateIntegral sing_114 5.htm#SEC1221sprintf1737 evalJacobianAtBox sing_2689.htm#SEC2765 42716 1738 evalPolyAtBox sing_2688.htm#SEC2764 43040 1739 evaluateFormalDivisor evaluateFormalDivisor sing_2366.htm#SEC2442 3535 1740 evaluatePDivisor sing_2372.htm#SEC2448 18855 1741 evaluateProduct sing_2442.htm#SEC2518 54515 1742 evaluate_reynolds sing_1650.htm#SEC1726 46353 1743 evalutateIntegral sing_1147.htm#SEC1223 sprintf 1748 1744 example sing_237.htm#SEC277 1749 example sing_219 3.htm#IDX8671750 example sing_219 4.htm#IDX8691751 example sing_219 5.htm#IDX8711752 example sing_219 6.htm#IDX8731753 example sing_219 7.htm#IDX8751754 example sing_2 198.htm#IDX8771755 example sing_2 199.htm#IDX8801745 example sing_2195.htm#IDX860 1746 example sing_2196.htm#IDX862 1747 example sing_2197.htm#IDX864 1748 example sing_2198.htm#IDX866 1749 example sing_2199.htm#IDX868 1750 example sing_2200.htm#IDX870 1751 example sing_2201.htm#IDX873 1756 1752 execute sing_238.htm#SEC278 1757 1753 exit sing_390.htm#SEC430 1758 exp2pt sing_185 1.htm#SEC1927196211759 expo sing_187 5.htm#SEC195188331760 exponents sing_220 3.htm#IDX8881754 exp2pt sing_1853.htm#SEC1929 19621 1755 expo sing_1877.htm#SEC1953 8833 1756 exponents sing_2205.htm#IDX881 1761 1757 export sing_383.htm#SEC423 1762 exportNuminvs sing_12 68.htm#SEC1344104231758 exportNuminvs sing_1270.htm#SEC1346 10423 1763 1759 exportto sing_384.htm#SEC424 1764 expp sing_273 1.htm#SEC2807157511760 expp sing_2738.htm#SEC2814 15751 1765 1761 expression list sing_72.htm#IDX128 1766 1762 expression list sing_422.htm#IDX299 1767 1763 ext-module purityfiltration_lib sing_758.htm#IDX368 1768 extcurve sing_179 7.htm#SEC187367301769 extdevelop sing_15 59.htm#SEC1635510441770 extendGC sing_932.htm#SEC1008 252291764 extcurve sing_1799.htm#SEC1875 6730 1765 extdevelop sing_1561.htm#SEC1637 51044 1766 extendGC sing_932.htm#SEC1008 40951 1771 1767 extendWeyl sing_792.htm#SEC844 49954 1772 1768 extendedTensor sing_724.htm#SEC776 4975 1773 1769 extendpoly sing_931.htm#SEC1007 29201 1774 extendring sing_10 08.htm#SEC1084647811775 extension of rings sing_132 1.htm#IDX5871776 exterior basis sing_107 5.htm#IDX5141777 exterior power sing_107 7.htm#IDX5161778 exteriorBasis sing_107 5.htm#SEC1151sprintf1779 exteriorPower sing_107 7.htm#SEC1153201731770 extendring sing_1010.htm#SEC1086 64781 1771 extension of rings sing_1323.htm#IDX580 1772 exterior basis sing_1077.htm#IDX507 1773 exterior power sing_1079.htm#IDX509 1774 exteriorBasis sing_1077.htm#SEC1153 sprintf 1775 exteriorPower sing_1079.htm#SEC1155 20173 1780 1776 extgcd sing_239.htm#SEC279 1781 fVector sing_205 7.htm#SEC213337151782 fVectorP sing_208 6.htm#SEC2162318431777 fVector sing_2059.htm#SEC2135 3715 1778 fVectorP sing_2088.htm#SEC2164 31843 1783 1779 facFirstShift sing_711.htm#SEC763 6469 1784 1780 facFirstWeyl sing_707.htm#SEC759 42412 1785 facGBIdeal sing_128 6.htm#SEC136299241781 facGBIdeal sing_1288.htm#SEC1364 9924 1786 1782 facShift sing_710.htm#SEC762 48551 1787 1783 facSubWeyl sing_709.htm#SEC761 9630 1788 1784 facWeyl sing_706.htm#SEC758 32331 1789 faceContaining sing_20 29.htm#SEC2105648041790 facetVertexLatticeDistances facetVertexLatticeDistances sing_208 7.htm#SEC2163607141791 facetWidth sing_20 88.htm#SEC2164628101792 facetWidths sing_20 89.htm#SEC216555031793 facets sing_203 0.htm#SEC210681121785 faceContaining sing_2031.htm#SEC2107 64804 1786 facetVertexLatticeDistances facetVertexLatticeDistances sing_2089.htm#SEC2165 60714 1787 facetWidth sing_2090.htm#SEC2166 62810 1788 facetWidths sing_2091.htm#SEC2167 5503 1789 facets sing_2032.htm#SEC2108 8112 1794 1790 facstd sing_240.htm#SEC280 1795 1791 factmodd sing_241.htm#SEC281 1796 1792 factor sing_322.htm#SEC362 1797 1793 factorH sing_922.htm#SEC998 24814 1798 factorLenstraECM sing_191 4.htm#SEC1990549511799 factorMain sing_175 1.htm#SEC1827651521800 factorgroup sing_257 0.htm#SEC2646599141794 factorLenstraECM sing_1916.htm#SEC1992 54951 1795 factorMain sing_1753.htm#SEC1829 65152 1796 factorgroup sing_2577.htm#SEC2653 59914 1801 1797 factorial sing_908.htm#SEC984 32871 1802 1798 factorization sing_323.htm#SEC363 1803 factorization sing_110 5.htm#IDX5181799 factorization sing_1107.htm#IDX511 1804 1800 factorize sing_242.htm#SEC282 1805 1801 factorize sing_322.htm#SEC362 1806 1802 factory sing_1.htm#IDX2 1807 1803 fan sing_189.htm#SEC229 1808 fan sing_20 69.htm#IDX8141809 fanViaCones sing_205 5.htm#SEC2131164181804 fan sing_2071.htm#IDX807 1805 fanViaCones sing_2057.htm#SEC2133 16418 1810 1806 farey sing_243.htm#SEC283 1811 fareypoly sing_23 69.htm#SEC2445123891812 fastExpt sing_18 59.htm#SEC1935439121807 fareypoly sing_2375.htm#SEC2451 12389 1808 fastExpt sing_1861.htm#SEC1937 43912 1813 1809 fastHC, option sing_315.htm#IDX153 1814 fastelim sing_171 3.htm#SEC178974091810 fastelim sing_1715.htm#SEC1791 7409 1815 1811 fetch sing_244.htm#SEC284 1816 1812 fetch (plural) sing_461.htm#SEC501 1817 fetchall sing_10 09.htm#SEC108575371818 ffmodStd sing_237 3.htm#SEC2449506801819 ffmodstd.lib sing_23 68.htm#SEC24441820 ffmodstd_lib sing_23 68.htm#SEC24441821 ffsolve sing_170 2.htm#SEC1778204321822 ffsolve.lib sing_170 1.htm#SEC17771823 ffsolve_lib sing_170 1.htm#SEC17771813 fetchall sing_1011.htm#SEC1087 7537 1814 ffmodStd sing_2379.htm#SEC2455 50680 1815 ffmodstd.lib sing_2374.htm#SEC2450 1816 ffmodstd_lib sing_2374.htm#SEC2450 1817 ffsolve sing_1704.htm#SEC1780 20432 1818 ffsolve.lib sing_1703.htm#SEC1779 1819 ffsolve_lib sing_1703.htm#SEC1779 1824 1820 fglm sing_245.htm#SEC285 1825 1821 fglm sing_355.htm#IDX187 1826 fglm_solve sing_17 29.htm#SEC1805513981822 fglm_solve sing_1731.htm#SEC1807 51398 1827 1823 fglmquot sing_246.htm#SEC286 1828 1824 fibonacci sing_909.htm#SEC985 24750 … … 1831 1827 filecmd sing_247.htm#SEC287 1832 1828 filtration purityfiltration_lib sing_758.htm#IDX369 1833 finalCharts sing_142 1.htm#SEC1497372961829 finalCharts sing_1423.htm#SEC1499 37296 1834 1830 find sing_248.htm#SEC288 1835 1831 findAuto sing_665.htm#SEC717 51205 1836 1832 findInvo sing_663.htm#SEC715 18177 1837 1833 findInvoDiag sing_664.htm#SEC716 7365 1838 findOrientedBoundary findOrientedBoundary sing_20 78.htm#SEC2154241101839 findTorsion sing_184 0.htm#SEC1916295721840 find_first_primitive_root find_first_primitive_root sing_19 18.htm#SEC1994333271841 find_index sing_192 2.htm#SEC1998625641842 findifs.lib sing_184 7.htm#SEC19231843 findifs_example sing_18 48.htm#SEC1924338491844 findifs_lib sing_184 7.htm#SEC19231834 findOrientedBoundary findOrientedBoundary sing_2080.htm#SEC2156 24110 1835 findTorsion sing_1842.htm#SEC1918 29572 1836 find_first_primitive_root find_first_primitive_root sing_1920.htm#SEC1996 33327 1837 find_index sing_1924.htm#SEC2000 62564 1838 findifs.lib sing_1849.htm#SEC1925 1839 findifs_example sing_1850.htm#SEC1926 33849 1840 findifs_lib sing_1849.htm#SEC1925 1845 1841 findimAlgebra sing_733.htm#SEC785 64612 1846 1842 finduni sing_249.htm#SEC289 1847 findvars sing_171 4.htm#SEC1790545031843 findvars sing_1716.htm#SEC1792 54503 1848 1844 finite field sing_144.htm#SEC184 1849 finite field sing_170 1.htm#IDX7871850 finiteDiagInvariants finiteDiagInvariants sing_126 3.htm#SEC133935081851 finitediff.lib sing_23 74.htm#IDX9811852 finitediff_lib sing_23 74.htm#IDX9821853 finitenessTest sing_11 19.htm#SEC1195406331854 finvar.lib sing_163 6.htm#SEC17121855 finvar_lib sing_163 6.htm#SEC17121845 finite field sing_1703.htm#IDX780 1846 finiteDiagInvariants finiteDiagInvariants sing_1265.htm#SEC1341 3508 1847 finitediff.lib sing_2380.htm#IDX978 1848 finitediff_lib sing_2380.htm#IDX979 1849 finitenessTest sing_1121.htm#SEC1197 40633 1850 finvar.lib sing_1638.htm#SEC1714 1851 finvar_lib sing_1638.htm#SEC1714 1856 1852 first index is 1 sing_417.htm#SEC457 1857 firstoct sing_176 2.htm#SEC1838114981858 fitting sing_116 5.htm#SEC1241206611859 fixed points, moduli space of stable maps, graph fixedPoints sing_272 1.htm#IDX10611860 fixedPoints sing_272 1.htm#SEC2797253661853 firstoct sing_1764.htm#SEC1840 11498 1854 fitting sing_1167.htm#SEC1243 20661 1855 fixed points, moduli space of stable maps, graph fixedPoints sing_2728.htm#IDX1059 1856 fixedPoints sing_2728.htm#SEC2804 25366 1861 1857 fl2poly sing_590.htm#SEC642 51682 1862 flatten sing_105 0.htm#SEC1126556171863 flatteningStrat sing_116 6.htm#SEC1242156221864 floating point sing_10 18.htm#IDX5041858 flatten sing_1052.htm#SEC1128 55617 1859 flatteningStrat sing_1168.htm#SEC1244 15622 1860 floating point sing_1020.htm#IDX497 1865 1861 for sing_385.htm#SEC425 1866 formaldivisorplus sing_236 1.htm#SEC2437319591867 forward sing_238 0.htm#SEC2456153831862 formaldivisorplus sing_2367.htm#SEC2443 31959 1863 forward sing_2386.htm#SEC2462 15383 1868 1864 fourier sing_585.htm#SEC637 5326 1869 fouriersystem sing_239 1.htm#SEC2467436811865 fouriersystem sing_2397.htm#SEC2473 43681 1870 1866 fpadim.lib sing_601.htm#SEC653 1871 1867 fpadim_lib sing_601.htm#SEC653 … … 1873 1869 fpaprops_lib sing_635.htm#SEC687 1874 1870 fprintf sing_251.htm#SEC291 13662 1875 fracStatus sing_265 0.htm#SEC2726145821876 frandwalk sing_2 694.htm#SEC2770255551877 free sing_220 2.htm#IDX8851878 free sing_220 3.htm#IDX8871871 fracStatus sing_2657.htm#SEC2733 14582 1872 frandwalk sing_2701.htm#SEC2777 25555 1873 free sing_2204.htm#IDX878 1874 free sing_2205.htm#IDX880 1879 1875 free associative algebra, tensor algebra Free associative algebras sing_492.htm#SEC544 1880 1876 freeGBasis sing_649.htm#SEC701 43055 1881 freeModule sing_24 87.htm#SEC2563341731882 freeModule2Module sing_25 16.htm#SEC2592152961877 freeModule sing_2494.htm#SEC2570 34173 1878 freeModule2Module sing_2523.htm#SEC2599 15296 1883 1879 freegb.lib sing_644.htm#SEC696 1884 1880 freegb_lib sing_644.htm#SEC696 1885 1881 freemodule sing_252.htm#SEC292 1886 freerank sing_96 6.htm#SEC1042522181882 freerank sing_968.htm#SEC1044 52218 1887 1883 fres sing_253.htm#SEC293 1888 from_boolean_constant from_boolean_constant sing_223 3.htm#SEC2309448811889 from_boolean_ideal sing_223 7.htm#SEC2313626981890 from_boolean_poly sing_223 4.htm#SEC2310278641891 from_boolean_set sing_22 38.htm#SEC2314606151884 from_boolean_constant from_boolean_constant sing_2235.htm#SEC2311 44881 1885 from_boolean_ideal sing_2239.htm#SEC2315 62698 1886 from_boolean_poly sing_2236.htm#SEC2312 27864 1887 from_boolean_set sing_2240.htm#SEC2316 60615 1892 1888 frwalk sing_254.htm#SEC294 1893 full representation sing_931.htm#IDX4 551894 full representation sing_932.htm#IDX4 611895 fullDimImages sing_24 17.htm#SEC2493200941896 fullFan sing_205 6.htm#SEC213275341889 full representation sing_931.htm#IDX446 1890 full representation sing_932.htm#IDX451 1891 fullDimImages sing_2423.htm#SEC2499 20094 1892 fullFan sing_2058.htm#SEC2134 7534 1897 1893 fullSerreRelations sing_659.htm#SEC711 27691 1898 fullSpace sing_201 1.htm#SEC2087194851899 furtherInvar sing_168 0.htm#SEC1756192091900 further_hn_proc sing_157 6.htm#SEC1652635001901 fwalk sing_115 2.htm#SEC1228150701894 fullSpace sing_2013.htm#SEC2089 19485 1895 furtherInvar sing_1682.htm#SEC1758 19209 1896 further_hn_proc sing_1578.htm#SEC1654 63500 1897 fwalk sing_1154.htm#SEC1230 15070 1902 1898 galois field sing_144.htm#SEC184 1903 gauss_col sing_106 0.htm#SEC1136362521904 gauss_nf sing_109 1.htm#SEC1167510601905 gauss_row sing_106 1.htm#SEC1137588771906 gaussred sing_10 89.htm#SEC1165290011907 gaussred_pivot sing_109 0.htm#SEC1166254771899 gauss_col sing_1062.htm#SEC1138 36252 1900 gauss_nf sing_1093.htm#SEC1169 51060 1901 gauss_row sing_1063.htm#SEC1139 58877 1902 gaussred sing_1091.htm#SEC1167 29001 1903 gaussred_pivot sing_1092.htm#SEC1168 25477 1908 1904 gcd sing_255.htm#SEC295 1909 gcdMon sing_119 4.htm#SEC1270424481910 gcddivisor sing_195 0.htm#SEC202612761905 gcdMon sing_1196.htm#SEC1272 42448 1906 gcddivisor sing_1952.htm#SEC2028 1276 1911 1907 gen sing_256.htm#SEC296 1912 genMDSMat sing_181 7.htm#SEC189333471913 genSymId sing_134 0.htm#SEC1416175211908 genMDSMat sing_1819.htm#SEC1895 3347 1909 genSymId sing_1342.htm#SEC1418 17521 1914 1910 general error-locator polynomial sing_887.htm#SEC952 1915 general neron. sing_24 45.htm#IDX9891911 general neron. sing_2451.htm#IDX986 1916 1912 general weighted lexicographical ordering sing_861.htm#IDX410 1917 1913 general weighted reverse lexicographical ordering Local orderings sing_861.htm#IDX407 1918 1914 general.lib sing_902.htm#SEC978 1919 generalOrder sing_197 5.htm#SEC2051425361915 generalOrder sing_1977.htm#SEC2053 42536 1920 1916 general_lib sing_902.htm#SEC978 1921 generateG sing_191 3.htm#SEC1989516971922 generators sing_147 6.htm#IDX6491923 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_203 1.htm#SEC210744541924 generatorsOfSpan sing_203 2.htm#SEC2108402971925 generic representation sing_931.htm#IDX4 541926 genericid sing_98 4.htm#SEC1060297311927 genericity sing_183 7.htm#SEC1913168221928 genericmat sing_105 1.htm#SEC1127350161929 genoutput sing_141 0.htm#SEC1486189731930 genus sing_124 5.htm#SEC1321sprintf1931 geometrical locus FamElemsAtEnvCompPoints sing_935.htm#IDX4 671932 geometrical locus sing_936.htm#IDX4 701933 geometrical locus sing_937.htm#IDX4 731934 geometrical locus sing_938.htm#IDX4 761935 geometrical locus sing_939.htm#IDX4 791936 geometrical locus sing_940.htm#IDX4 811937 geometrical locus sing_941.htm#IDX4 851938 getArguments sing_104 1.htm#SEC1117142541939 getCommand sing_104 0.htm#SEC1116321811940 getCone sing_20 58.htm#SEC2134413941941 getGradingGroup sing_25 45.htm#SEC2621181371942 getLattice sing_25 46.htm#SEC262277751943 getLinearForms sing_203 3.htm#SEC2109475901944 getModuleGrading sing_25 56.htm#SEC2632434511945 getMultiplicity sing_203 4.htm#SEC21106391946 getOneVar sing_125 3.htm#SEC1329554021947 getResult sing_104 2.htm#SEC1118517221948 getSmallest sing_125 2.htm#SEC132816231949 getState sing_104 3.htm#SEC1119364531950 getVariableWeights sing_25 44.htm#SEC262095911951 getcores sing_ 999.htm#SEC1075307851917 generateG sing_1915.htm#SEC1991 51697 1918 generators sing_1478.htm#IDX642 1919 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2033.htm#SEC2109 4454 1920 generatorsOfSpan sing_2034.htm#SEC2110 40297 1921 generic representation sing_931.htm#IDX445 1922 genericid sing_986.htm#SEC1062 29731 1923 genericity sing_1839.htm#SEC1915 16822 1924 genericmat sing_1053.htm#SEC1129 35016 1925 genoutput sing_1412.htm#SEC1488 18973 1926 genus sing_1247.htm#SEC1323 sprintf 1927 geometrical locus FamElemsAtEnvCompPoints sing_935.htm#IDX457 1928 geometrical locus sing_936.htm#IDX460 1929 geometrical locus sing_937.htm#IDX463 1930 geometrical locus sing_938.htm#IDX466 1931 geometrical locus sing_939.htm#IDX469 1932 geometrical locus sing_940.htm#IDX471 1933 geometrical locus sing_941.htm#IDX475 1934 getArguments sing_1043.htm#SEC1119 14254 1935 getCommand sing_1042.htm#SEC1118 32181 1936 getCone sing_2060.htm#SEC2136 41394 1937 getGradingGroup sing_2552.htm#SEC2628 18137 1938 getLattice sing_2553.htm#SEC2629 7775 1939 getLinearForms sing_2035.htm#SEC2111 47590 1940 getModuleGrading sing_2563.htm#SEC2639 43451 1941 getMultiplicity sing_2036.htm#SEC2112 639 1942 getOneVar sing_1255.htm#SEC1331 55402 1943 getResult sing_1044.htm#SEC1120 51722 1944 getSmallest sing_1254.htm#SEC1330 1623 1945 getState sing_1045.htm#SEC1121 36453 1946 getVariableWeights sing_2551.htm#SEC2627 9591 1947 getcores sing_1001.htm#SEC1077 30785 1952 1948 getdump sing_257.htm#SEC297 1953 1949 getenv sing_358.htm#IDX211 1954 gfan.lib sing_201 0.htm#SEC20861955 gfan_lib sing_201 0.htm#SEC20861950 gfan.lib sing_2012.htm#SEC2088 1951 gfan_lib sing_2012.htm#SEC2088 1956 1952 gfanlib sing_1.htm#IDX9 1957 gitCone sing_24 44.htm#SEC2520238531958 gitfan.lib sing_24 14.htm#SEC24901959 gitfan_lib sing_24 14.htm#SEC24901953 gitCone sing_2450.htm#SEC2526 23853 1954 gitfan.lib sing_2420.htm#SEC2496 1955 gitfan_lib sing_2420.htm#SEC2496 1960 1956 gkdim.lib sing_670.htm#SEC722 1961 1957 gkdim_lib sing_670.htm#SEC722 … … 1964 1960 global Bernstein-Sato polynomial sing_540.htm#IDX331 1965 1961 global Bernstein-Sato polynomial for variety sing_596.htm#IDX356 1966 globalSections sing_23 55.htm#SEC2431551911967 gmscoeffs sing_153 4.htm#SEC1610131821968 gmsnf sing_153 3.htm#SEC1609446761969 gmspoly.lib sing_155 3.htm#SEC16291970 gmspoly_lib sing_155 3.htm#SEC16291971 gmsring sing_153 2.htm#SEC1608594381972 gmssing.lib sing_153 1.htm#SEC16071973 gmssing_lib sing_153 1.htm#SEC16071974 goettsche.lib sing_2 398.htm#SEC24741975 goettsche_lib sing_2 398.htm#SEC24741976 good basis sing_153 1.htm#IDX6771977 good basis sing_154 1.htm#IDX7321978 good basis sing_155 3.htm#IDX7481979 good basis sing_155 5.htm#IDX7591980 goodBasis sing_155 5.htm#SEC1631416061981 gorensteinIndex sing_209 0.htm#SEC2166529191982 gorensteinVector sing_209 1.htm#SEC2167504071983 graal.lib sing_24 07.htm#SEC24831984 graalMixed sing_24 08.htm#SEC248464011985 graal_lib sing_24 07.htm#SEC24831962 globalSections sing_2361.htm#SEC2437 55191 1963 gmscoeffs sing_1536.htm#SEC1612 13182 1964 gmsnf sing_1535.htm#SEC1611 44676 1965 gmspoly.lib sing_1555.htm#SEC1631 1966 gmspoly_lib sing_1555.htm#SEC1631 1967 gmsring sing_1534.htm#SEC1610 59438 1968 gmssing.lib sing_1533.htm#SEC1609 1969 gmssing_lib sing_1533.htm#SEC1609 1970 goettsche.lib sing_2404.htm#SEC2480 1971 goettsche_lib sing_2404.htm#SEC2480 1972 good basis sing_1533.htm#IDX670 1973 good basis sing_1543.htm#IDX725 1974 good basis sing_1555.htm#IDX741 1975 good basis sing_1557.htm#IDX752 1976 goodBasis sing_1557.htm#SEC1633 41606 1977 gorensteinIndex sing_2092.htm#SEC2168 52919 1978 gorensteinVector sing_2093.htm#SEC2169 50407 1979 graal.lib sing_2413.htm#SEC2489 1980 graalMixed sing_2414.htm#SEC2490 6401 1981 graal_lib sing_2413.htm#SEC2489 1986 1982 gradeNumber sing_762.htm#SEC814 29956 1987 1983 graded Weyl algebra sing_505.htm#IDX316 1988 graded algebra sing_224 4.htm#IDX9401989 graded module, graded piece sing_145 7.htm#IDX6351990 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_24 47.htm#IDX9901984 graded algebra sing_2246.htm#IDX933 1985 graded module, graded piece sing_1459.htm#IDX628 1986 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2453.htm#IDX987 1991 1987 graded modules, handling of Handling graded modules sing_826.htm#SEC878 1992 graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism modules_lib sing_24 84.htm#IDX9911993 gradedModules.lib sing_24 47.htm#SEC25231994 gradedModules_lib sing_24 47.htm#SEC25231995 gradiator sing_25 89.htm#SEC2665538021996 graph sing_114 1.htm#IDX5311997 graph sing_114 2.htm#IDX5321998 graph sing_27 16.htm#IDX10561999 graph sing_27 17.htm#IDX10572000 graphics.lib sing_176 4.htm#SEC18402001 graphics_lib sing_176 4.htm#SEC18401988 graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism modules_lib sing_2491.htm#IDX989 1989 gradedModules.lib sing_2453.htm#SEC2529 1990 gradedModules_lib sing_2453.htm#SEC2529 1991 gradiator sing_2596.htm#SEC2672 53802 1992 graph sing_1143.htm#IDX524 1993 graph sing_1144.htm#IDX525 1994 graph sing_2723.htm#IDX1054 1995 graph sing_2724.htm#IDX1055 1996 graphics.lib sing_1766.htm#SEC1842 1997 graphics_lib sing_1766.htm#SEC1842 2002 1998 graphviz sing_1.htm#IDX13 2003 graver4ti2 sing_13 38.htm#SEC1414396352004 grconcat sing_247 0.htm#SEC2546167542005 grdeg sing_245 0.htm#SEC2526228792006 grgens sing_24 59.htm#SEC2535128232007 grgroebner sing_24 69.htm#SEC2545292882008 grlift sing_24 67.htm#SEC2543216562009 grlifting sing_24 74.htm#SEC2550511772010 grlifting2 sing_24 75.htm#SEC2551590112011 grlifting3 sing_24 77.htm#SEC255363692012 grneg sing_248 0.htm#SEC2556645841999 graver4ti2 sing_1340.htm#SEC1416 39635 2000 grconcat sing_2476.htm#SEC2552 16754 2001 grdeg sing_2456.htm#SEC2532 22879 2002 grgens sing_2465.htm#SEC2541 12823 2003 grgroebner sing_2475.htm#SEC2551 29288 2004 grlift sing_2473.htm#SEC2549 21656 2005 grlifting sing_2480.htm#SEC2556 51177 2006 grlifting2 sing_2481.htm#SEC2557 59011 2007 grlifting3 sing_2483.htm#SEC2559 6369 2008 grneg sing_2486.htm#SEC2562 64584 2013 2009 grobcov sing_924.htm#SEC1000 44826 2014 2010 grobcov.lib sing_923.htm#SEC999 2015 2011 grobcov_lib sing_923.htm#SEC999 2016 grobj sing_24 48.htm#SEC2524181152012 grobj sing_2454.htm#SEC2530 18115 2017 2013 groebner sing_258.htm#SEC298 53038 2018 2014 groebner sing_818.htm#SEC870 2019 2015 groebner basis computations sing_258.htm#IDX147 2020 groebnerComplex sing_21 69.htm#SEC224524212021 groebnerCone sing_216 3.htm#SEC2239587762022 groebnerFan sing_21 68.htm#SEC2244481572023 gromovWitten sing_114 6.htm#SEC1222285592024 grorder sing_246 1.htm#SEC2537208572016 groebnerComplex sing_2171.htm#SEC2247 2421 2017 groebnerCone sing_2165.htm#SEC2241 58776 2018 groebnerFan sing_2170.htm#SEC2246 48157 2019 gromovWitten sing_1148.htm#SEC1224 28559 2020 grorder sing_2467.htm#SEC2543 20857 2025 2021 ground field sing_144.htm#SEC184 2026 groupActionOnHashes sing_243 2.htm#SEC25084062027 groupActionOnQImage sing_243 1.htm#SEC2507532702028 group_reynolds sing_164 4.htm#SEC1720350792029 grpower sing_24 57.htm#SEC253339602030 grpres sing_246 0.htm#SEC2536181452031 grprod sing_24 68.htm#SEC2544415252032 grrange sing_24 79.htm#SEC2555418352033 grres sing_24 66.htm#SEC2542357952034 grrndmap sing_247 2.htm#SEC254840542035 grrndmap2 sing_247 3.htm#SEC2549505362036 grrndmat sing_247 1.htm#SEC2547426342037 grshift sing_245 2.htm#SEC252814152038 grsum sing_24 56.htm#SEC2532606022039 grsyz sing_24 65.htm#SEC2541618432040 grtest sing_24 49.htm#SEC2525625772041 grtranspose sing_24 58.htm#SEC2534138652042 grtranspose1 sing_246 2.htm#SEC253836372043 grtwist sing_24 54.htm#SEC2530104982044 grtwists sing_24 55.htm#SEC2531566382045 grview sing_245 1.htm#SEC252768782046 grwalk.lib sing_115 1.htm#SEC12272047 grwalk_lib sing_115 1.htm#SEC12272048 grzero sing_245 3.htm#SEC252942122049 gwalk sing_115 7.htm#SEC1233382382050 hStarVector sing_209 2.htm#SEC2168608212051 hVector sing_209 3.htm#SEC2169464862052 h_increasing_knapsack h_increasing_knapsack sing_193 6.htm#SEC2012629682022 groupActionOnHashes sing_2438.htm#SEC2514 406 2023 groupActionOnQImage sing_2437.htm#SEC2513 53270 2024 group_reynolds sing_1646.htm#SEC1722 35079 2025 grpower sing_2463.htm#SEC2539 3960 2026 grpres sing_2466.htm#SEC2542 18145 2027 grprod sing_2474.htm#SEC2550 41525 2028 grrange sing_2485.htm#SEC2561 41835 2029 grres sing_2472.htm#SEC2548 35795 2030 grrndmap sing_2478.htm#SEC2554 4054 2031 grrndmap2 sing_2479.htm#SEC2555 50536 2032 grrndmat sing_2477.htm#SEC2553 42634 2033 grshift sing_2458.htm#SEC2534 1415 2034 grsum sing_2462.htm#SEC2538 60602 2035 grsyz sing_2471.htm#SEC2547 61843 2036 grtest sing_2455.htm#SEC2531 62577 2037 grtranspose sing_2464.htm#SEC2540 13865 2038 grtranspose1 sing_2468.htm#SEC2544 3637 2039 grtwist sing_2460.htm#SEC2536 10498 2040 grtwists sing_2461.htm#SEC2537 56638 2041 grview sing_2457.htm#SEC2533 6878 2042 grwalk.lib sing_1153.htm#SEC1229 2043 grwalk_lib sing_1153.htm#SEC1229 2044 grzero sing_2459.htm#SEC2535 4212 2045 gwalk sing_1159.htm#SEC1235 38238 2046 hStarVector sing_2094.htm#SEC2170 60821 2047 hVector sing_2095.htm#SEC2171 46486 2048 h_increasing_knapsack h_increasing_knapsack sing_1938.htm#SEC2014 62968 2053 2049 hardware platform sing_358.htm#IDX271 2054 hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_102 2.htm#SEC1098546092055 hasCommutativeVars sing_10 19.htm#SEC109531522056 hasGlobalOrdering sing_102 0.htm#SEC1096340532057 hasLeftDenom sing_2 598.htm#SEC2674472602058 hasMixedOrdering sing_102 1.htm#SEC1097297382059 hasNumericCoeffs sing_10 18.htm#SEC1094145222060 hasRightDenom sing_2 599.htm#SEC2675342792061 hasTransExtensionCoefficient hasTransExtensionCoefficient sing_102 3.htm#SEC1099562112062 hashToCone sing_244 2.htm#SEC251869292063 hashesToFan sing_244 3.htm#SEC2519267742064 headStand sing_107 3.htm#SEC1149144132065 heightZ sing_131 5.htm#SEC1391168002050 hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1024.htm#SEC1100 54609 2051 hasCommutativeVars sing_1021.htm#SEC1097 3152 2052 hasGlobalOrdering sing_1022.htm#SEC1098 34053 2053 hasLeftDenom sing_2605.htm#SEC2681 47260 2054 hasMixedOrdering sing_1023.htm#SEC1099 29738 2055 hasNumericCoeffs sing_1020.htm#SEC1096 14522 2056 hasRightDenom sing_2606.htm#SEC2682 34279 2057 hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1025.htm#SEC1101 56211 2058 hashToCone sing_2448.htm#SEC2524 6929 2059 hashesToFan sing_2449.htm#SEC2525 26774 2060 headStand sing_1075.htm#SEC1151 14413 2061 heightZ sing_1317.htm#SEC1393 16800 2066 2062 help sing_259.htm#SEC299 2067 2063 help browsers The online help system sing_16.htm#IDX22 … … 2074 2070 help, accessing over the net Command line options sing_19.htm#IDX42 2075 2071 help, online help system The online help system sing_16.htm#SEC22 2076 hermiteNormalForm sing_259 0.htm#SEC2666372252077 hess.lib sing_248 2.htm#SEC25582078 hess_lib sing_248 2.htm#SEC25582072 hermiteNormalForm sing_2597.htm#SEC2673 37225 2073 hess.lib sing_2488.htm#SEC2564 2074 hess_lib sing_2488.htm#SEC2564 2079 2075 hessenberg sing_358.htm#IDX217 24168 2080 hessenberg sing_109 5.htm#SEC11712076 hessenberg sing_1097.htm#SEC1173 2081 2077 highcorner sing_260.htm#SEC300 2082 2078 hilb sing_261.htm#SEC301 2083 hilbPoly sing_98 2.htm#SEC1058361182084 hilbert4ti2 sing_133 7.htm#SEC1413139932085 hilbertBasis sing_209 4.htm#SEC2170354232086 hilbertSeries sing_259 2.htm#SEC2668601482087 hilbvec sing_171 5.htm#SEC179192042088 hnexpansion sing_155 7.htm#SEC1633469902089 hnoether.lib sing_155 6.htm#SEC16322090 hnoether_lib sing_155 6.htm#SEC16322079 hilbPoly sing_984.htm#SEC1060 36118 2080 hilbert4ti2 sing_1339.htm#SEC1415 13993 2081 hilbertBasis sing_2096.htm#SEC2172 35423 2082 hilbertSeries sing_2599.htm#SEC2675 60148 2083 hilbvec sing_1717.htm#SEC1793 9204 2084 hnexpansion sing_1559.htm#SEC1635 46990 2085 hnoether.lib sing_1558.htm#SEC1634 2086 hnoether_lib sing_1558.htm#SEC1634 2091 2087 holonomic rank sing_780.htm#IDX380 2092 2088 holonomicRank sing_784.htm#SEC836 41306 2093 hom sing_25 28.htm#SEC2604400322094 hom_kernel sing_117 3.htm#SEC1249326042089 hom sing_2535.htm#SEC2611 40032 2090 hom_kernel sing_1175.htm#SEC1251 32604 2095 2091 homog sing_262.htm#SEC302 2096 homog_part sing_27 28.htm#SEC2804208752097 homog_parts sing_27 29.htm#SEC2805128542098 homogeneitySpace sing_216 5.htm#SEC2241482432092 homog_part sing_2735.htm#SEC2811 20875 2093 homog_parts sing_2736.htm#SEC2812 12854 2094 homogeneitySpace sing_2167.htm#SEC2243 48243 2099 2095 homogfacFirstQWeyl sing_713.htm#SEC765 32751 2100 2096 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_715.htm#SEC767 9014 2101 2097 homogfacNthQWeyl sing_712.htm#SEC764 19238 2102 2098 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_714.htm#SEC766 56179 2103 homolog.lib sing_11 58.htm#SEC12342104 homolog_lib sing_11 58.htm#SEC12342105 homology sing_11 68.htm#SEC1244150402106 homomorphism sing_251 2.htm#SEC2588271152107 howto, download Download instructions sing_27 55.htm#SEC28442108 howto, install on Macintosh Macintosh installation instructions sing_27 58.htm#SEC28472109 howto, install on Unix Unix installation instructions sing_27 56.htm#SEC28452110 howto, install on Windows Windows installation instructions sing_27 57.htm#SEC28462099 homolog.lib sing_1160.htm#SEC1236 2100 homolog_lib sing_1160.htm#SEC1236 2101 homology sing_1170.htm#SEC1246 15040 2102 homomorphism sing_2519.htm#SEC2595 27115 2103 howto, download Download instructions sing_2762.htm#SEC2851 2104 howto, install on Macintosh Macintosh installation instructions sing_2765.htm#SEC2854 2105 howto, install on Unix Unix installation instructions sing_2763.htm#SEC2852 2106 howto, install on Windows Windows installation instructions sing_2764.htm#SEC2853 2111 2107 hres sing_263.htm#SEC303 2112 2108 html, default help The online help system sing_16.htm#IDX24 2113 hyperel.lib sing_194 3.htm#SEC20192114 hyperel_lib sing_194 3.htm#SEC20192115 hyperplane sing_217 2.htm#IDX8252109 hyperel.lib sing_1945.htm#SEC2021 2110 hyperel_lib sing_1945.htm#SEC2021 2111 hyperplane sing_2174.htm#IDX818 2116 2112 hyperplane arrangement sing_540.htm#IDX337 2117 hypersurface singularity sing_158 3.htm#IDX7772118 iMult sing_12 48.htm#SEC1324220592119 id sing_24 85.htm#SEC2561475922120 id2mod sing_9 78.htm#SEC1054329182113 hypersurface singularity sing_1585.htm#IDX770 2114 iMult sing_1250.htm#SEC1326 22059 2115 id sing_2492.htm#SEC2568 47592 2116 id2mod sing_980.htm#SEC1056 32918 2121 2117 ideal sing_90.htm#SEC130 2122 2118 ideal declarations sing_91.htm#SEC131 … … 2129 2125 ideal related functions (plural) ideal related functions (plural) sing_427.htm#SEC467 2130 2126 ideal, toric sing_874.htm#SEC931 2131 idealSplit sing_172 2.htm#SEC179846732127 idealSplit sing_1724.htm#SEC1800 4673 2132 2128 ideals Miscellaneous oddities sing_418.htm#IDX293 2133 idealsimplify sing_148 4.htm#SEC1560385692129 idealsimplify sing_1486.htm#SEC1562 38569 2134 2130 identifier Identifier resolution sing_419.htm#SEC459 2135 identifyvar sing_139 2.htm#SEC1468596622131 identifyvar sing_1394.htm#SEC1470 59662 2136 2132 if sing_386.htm#SEC426 2137 image sing_25 08.htm#SEC2584434812138 imageLattice sing_25 58.htm#SEC2634157402139 image_of_variety sing_167 2.htm#SEC1748437112133 image sing_2515.htm#SEC2591 43481 2134 imageLattice sing_2565.htm#SEC2641 15740 2135 image_of_variety sing_1674.htm#SEC1750 43711 2140 2136 imap sing_264.htm#SEC304 2141 2137 imap (plural) sing_462.htm#SEC502 2142 imapall sing_101 0.htm#SEC1086160232138 imapall sing_1012.htm#SEC1088 16023 2143 2139 impart sing_265.htm#SEC305 2144 2140 importfrom sing_387.htm#SEC427 … … 2146 2142 inCentralizer sing_530.htm#SEC582 49000 2147 2143 inForm sing_572.htm#SEC624 5283 2148 inSubring sing_111 1.htm#SEC1187248172149 indSet sing_122 0.htm#SEC1296328282144 inSubring sing_1113.htm#SEC1189 24817 2145 indSet sing_1222.htm#SEC1298 32828 2150 2146 indepSet sing_266.htm#SEC306 2151 2147 indexed names sing_36.htm#IDX82 2152 2148 indexed names sing_37.htm#SEC65 2153 2149 indices, multi sing_37.htm#SEC65 2154 inequalities sing_203 5.htm#SEC2111101222150 inequalities sing_2037.htm#SEC2113 10122 2155 2151 infRedTail, option sing_315.htm#IDX154 2156 2152 info The online help system sing_16.htm#SEC23 2157 iniD sing_141 2.htm#SEC1488350842158 init_debug sing_149 1.htm#SEC1567298632159 initial sing_216 6.htm#SEC224286782153 iniD sing_1414.htm#SEC1490 35084 2154 init_debug sing_1493.htm#SEC1569 29863 2155 initial sing_2168.htm#SEC2244 8678 2160 2156 initial form sing_505.htm#IDX318 2161 2157 initial ideal sing_505.htm#IDX317 2162 2158 initial ideal approach sing_505.htm#IDX321 2163 2159 initial ideal approach sing_596.htm#IDX360 2164 initialForm sing_214 3.htm#SEC2219577932165 initialIdeal sing_214 4.htm#SEC2220222052160 initialForm sing_2145.htm#SEC2221 57793 2161 initialIdeal sing_2146.htm#SEC2222 22205 2166 2162 initialIdealW sing_571.htm#SEC623 36086 2167 2163 initialMalgrange sing_570.htm#SEC622 26846 2168 injective_knapsack sing_193 7.htm#SEC201376192169 inout.lib sing_94 4.htm#SEC10202170 inout_lib sing_94 4.htm#SEC10202164 injective_knapsack sing_1939.htm#SEC2015 7619 2165 inout.lib sing_946.htm#SEC1022 2166 inout_lib sing_946.htm#SEC1022 2171 2167 input sing_41.htm#SEC71 2172 2168 insert sing_126.htm#SEC166 2173 2169 insert sing_267.htm#SEC307 2174 insertCone sing_20 59.htm#SEC2135138582170 insertCone sing_2061.htm#SEC2137 13858 2175 2171 insertGenerator sing_591.htm#SEC643 13951 2176 instructions, Macintosh installation Macintosh installation instructions sing_27 58.htm#SEC28472177 instructions, Unix installation Unix installation instructions sing_27 56.htm#SEC28452178 instructions, Windows installation Windows installation instructions sing_27 57.htm#SEC28462179 instructions, downloading Download instructions sing_27 55.htm#SEC28442172 instructions, Macintosh installation Macintosh installation instructions sing_2765.htm#SEC2854 2173 instructions, Unix installation Unix installation instructions sing_2763.htm#SEC2852 2174 instructions, Windows installation Windows installation instructions sing_2764.htm#SEC2853 2175 instructions, downloading Download instructions sing_2762.htm#SEC2851 2180 2176 int sing_95.htm#SEC135 2181 2177 int declarations sing_96.htm#SEC136 … … 2183 2179 int operations sing_98.htm#SEC138 2184 2180 int related functions int related functions sing_99.htm#SEC139 2185 intInverse sing_25 67.htm#SEC2643sprintf2186 intPart sing_189 1.htm#SEC1967483602187 intRank sing_25 59.htm#SEC263518302188 intRoot sing_189 2.htm#SEC1968545822181 intInverse sing_2574.htm#SEC2650 sprintf 2182 intPart sing_1893.htm#SEC1969 48360 2183 intRank sing_2566.htm#SEC2642 1830 2184 intRoot sing_1894.htm#SEC1970 54582 2189 2185 intRoots sing_588.htm#SEC640 24538 2190 2186 intStrategy, option sing_315.htm#IDX155 2191 intclMonIdeal sing_126 1.htm#SEC1337223382192 intclToricRing sing_125 7.htm#SEC1333621432187 intclMonIdeal sing_1263.htm#SEC1339 22338 2188 intclToricRing sing_1259.htm#SEC1335 62143 2193 2189 integer division Miscellaneous oddities sing_418.htm#IDX288 2194 2190 integer programming sing_882.htm#SEC939 2195 integral sing_27 03.htm#SEC2779626832196 integral basis sing_118 0.htm#IDX5532197 integral basis sing_137 5.htm#IDX6202198 integral closure sing_124 1.htm#IDX5682199 integral closure sing_124 2.htm#IDX5712200 integral closure sing_124 3.htm#IDX5742201 integral closure sing_125 6.htm#IDX5802202 integralBasis sing_118 0.htm#SEC1256381142191 integral sing_2710.htm#SEC2786 62683 2192 integral basis sing_1182.htm#IDX546 2193 integral basis sing_1377.htm#IDX613 2194 integral closure sing_1243.htm#IDX561 2195 integral closure sing_1244.htm#IDX564 2196 integral closure sing_1245.htm#IDX567 2197 integral closure sing_1258.htm#IDX573 2198 integralBasis sing_1182.htm#SEC1258 38114 2203 2199 integralIdeal sing_575.htm#SEC627 29194 2204 2200 integralModule sing_576.htm#SEC628 58078 2205 integralSection sing_25 68.htm#SEC2644sprintf2206 integralbasis.lib sing_11 79.htm#SEC12552207 integralbasis_lib sing_11 79.htm#SEC12552201 integralSection sing_2575.htm#SEC2651 sprintf 2202 integralbasis.lib sing_1181.htm#SEC1257 2203 integralbasis_lib sing_1181.htm#SEC1257 2208 2204 integration of D-module sing_563.htm#IDX349 2209 2205 interface, Emacs Emacs user interface sing_21.htm#SEC28 2210 interiorLatticePoints interiorLatticePoints sing_209 5.htm#SEC2171498682211 internalfunctions sing_149 2.htm#SEC1568612302212 interpolate sing_17 28.htm#SEC1804515022206 interiorLatticePoints interiorLatticePoints sing_2097.htm#SEC2173 49868 2207 internalfunctions sing_1494.htm#SEC1570 61230 2208 interpolate sing_1730.htm#SEC1806 51502 2213 2209 interpolation sing_268.htm#SEC308 2214 interpret sing_253 0.htm#SEC2606484992215 interpretElem sing_25 33.htm#SEC2609517402216 interpretInv sing_253 1.htm#SEC260761492217 interpretList sing_25 34.htm#SEC2610640612210 interpret sing_2537.htm#SEC2613 48499 2211 interpretElem sing_2540.htm#SEC2616 51740 2212 interpretInv sing_2538.htm#SEC2614 6149 2213 interpretList sing_2541.htm#SEC2617 64061 2218 2214 interred sing_269.htm#SEC309 2219 2215 intersect sing_270.htm#SEC310 2220 2216 intersect (plural) sing_463.htm#SEC503 2221 2217 intersectElim, option sing_315.htm#IDX173 2222 intersectLattices sing_2564.htm#SEC2640 41354 2223 intersectMon sing_1197.htm#SEC1273 44572 2224 intersectOrbitsWithMovingCone intersectOrbitsWithMovingCone sing_2430.htm#SEC2506 19444 2218 intersectLattices sing_2571.htm#SEC2647 41354 2219 intersectLists sing_2343.htm#SEC2419 4153 2220 intersectMon sing_1199.htm#SEC1275 44572 2221 intersectOrbitsWithMovingCone intersectOrbitsWithMovingCone sing_2436.htm#SEC2512 19444 2225 2222 intersectSyz, option sing_315.htm#IDX174 2226 intersectZ sing_1317.htm#SEC1393 sprintf 2227 intersection sing_1566.htm#SEC1642 46938 2228 intersection lattice sing_2208.htm#IDX900 2229 intersection lattice sing_2209.htm#IDX901 2230 intersection multiplicity sing_1477.htm#IDX655 2231 intersection multiplicity sing_1566.htm#IDX770 2232 intersectionDiv sing_1440.htm#SEC1516 29017 2233 intersectionValRingIdeals intersectionValRingIdeals sing_1266.htm#SEC1342 38773 2234 intersectionValRings intersectionValRings sing_1265.htm#SEC1341 35761 2235 interval arithmetic sing_2673.htm#IDX1031 2223 intersectZ sing_1319.htm#SEC1395 sprintf 2224 intersection sing_1568.htm#SEC1644 46938 2225 intersection lattice sing_2210.htm#IDX893 2226 intersection lattice sing_2211.htm#IDX894 2227 intersection multiplicity sing_1479.htm#IDX648 2228 intersection multiplicity sing_1568.htm#IDX763 2229 intersectionDiv sing_1442.htm#SEC1518 29017 2230 intersectionValRingIdeals intersectionValRingIdeals sing_1268.htm#SEC1344 38773 2231 intersectionValRings intersectionValRings sing_1267.htm#SEC1343 35761 2232 intersectpar sing_944.htm#SEC1020 2975 2233 interval arithmetic sing_2680.htm#IDX1029 2236 2234 intmat sing_102.htm#SEC142 2237 2235 intmat declarations sing_103.htm#SEC143 … … 2240 2238 intmat related functions intmat related functions sing_107.htm#SEC147 2241 2239 intmat type cast sing_105.htm#SEC145 2242 intmat2mons sing_128 1.htm#SEC1357211502243 intprog.lib sing_118 1.htm#SEC12572244 intprog_lib sing_118 1.htm#SEC12572240 intmat2mons sing_1283.htm#SEC1359 21150 2241 intprog.lib sing_1183.htm#SEC1259 2242 intprog_lib sing_1183.htm#SEC1259 2245 2243 intvec sing_108.htm#SEC148 2246 2244 intvec declarations sing_109.htm#SEC149 … … 2248 2246 intvec operations sing_111.htm#SEC151 2249 2247 intvec related functions intvec related functions sing_112.htm#SEC152 2250 invariant sing_234 3.htm#IDX9582251 invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_164 1.htm#IDX7832252 invariant ring minimal generating set permutation group invariant_algebra_perm sing_164 2.htm#IDX7842253 invariantRing sing_167 4.htm#SEC1750185822254 invariant_algebra_perm invariant_algebra_perm sing_164 2.htm#SEC1718635252255 invariant_algebra_reynolds invariant_algebra_reynolds sing_164 1.htm#SEC1717357052256 invariant_basis sing_16 49.htm#SEC1725183432257 invariant_basis_reynolds invariant_basis_reynolds sing_165 0.htm#SEC1726547882258 invariant_ring sing_163 7.htm#SEC171380592259 invariant_ring_random invariant_ring_random sing_16 38.htm#SEC171469862260 invariants curveColengthDerivations sing_156 2.htm#SEC1638574992261 invariants sing_234 0.htm#IDX9512262 invariants sing_23 44.htm#IDX9602263 inverse sing_10 79.htm#SEC1155274112248 invariant sing_2349.htm#IDX955 2249 invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1643.htm#IDX776 2250 invariant ring minimal generating set permutation group invariant_algebra_perm sing_1644.htm#IDX777 2251 invariantRing sing_1676.htm#SEC1752 18582 2252 invariant_algebra_perm invariant_algebra_perm sing_1644.htm#SEC1720 63525 2253 invariant_algebra_reynolds invariant_algebra_reynolds sing_1643.htm#SEC1719 35705 2254 invariant_basis sing_1651.htm#SEC1727 18343 2255 invariant_basis_reynolds invariant_basis_reynolds sing_1652.htm#SEC1728 54788 2256 invariant_ring sing_1639.htm#SEC1715 8059 2257 invariant_ring_random invariant_ring_random sing_1640.htm#SEC1716 6986 2258 invariants curveColengthDerivations sing_1564.htm#SEC1640 57499 2259 invariants sing_2346.htm#IDX948 2260 invariants sing_2350.htm#IDX957 2261 inverse sing_1081.htm#SEC1157 27411 2264 2262 inverse of a matrix via its LU-decomposition sing_290.htm#SEC330 2265 2263 inverseFourier sing_586.htm#SEC638 65140 2266 inverse_B sing_108 0.htm#SEC1156176162267 inverse_L sing_108 1.htm#SEC1157492712268 inverse_modulus sing_192 0.htm#SEC1996608222269 invertBirMap sing_137 6.htm#SEC1452160862270 invertLeftFraction sing_266 0.htm#SEC2736519032271 invertNcfrac sing_26 08.htm#SEC2684508422272 invertNumberMain sing_175 2.htm#SEC1828626152264 inverse_B sing_1082.htm#SEC1158 17616 2265 inverse_L sing_1083.htm#SEC1159 49271 2266 inverse_modulus sing_1922.htm#SEC1998 60822 2267 invertBirMap sing_1378.htm#SEC1454 16086 2268 invertLeftFraction sing_2667.htm#SEC2743 51903 2269 invertNcfrac sing_2615.htm#SEC2691 50842 2270 invertNumberMain sing_1754.htm#SEC1830 62615 2273 2271 involut.lib sing_662.htm#SEC714 2274 2272 involut_lib sing_662.htm#SEC714 2275 2273 involution sing_667.htm#SEC719 34280 2276 invunit sing_158 5.htm#SEC1661623982277 iostruct sing_18 39.htm#SEC1915604442278 irrRealizationDim sing_212 5.htm#SEC220178142279 irred_secondary_char0 irred_secondary_char0 sing_166 3.htm#SEC173929432280 irred_secondary_no_molien irred_secondary_no_molien sing_166 6.htm#SEC1742559052281 irreddecMon sing_120 6.htm#SEC1282201602282 irreducible power series sing_156 7.htm#IDX7712283 irreducible secondary invariant irred_secondary_char0 sing_166 3.htm#IDX7852284 isAface sing_24 15.htm#SEC2491253442274 invunit sing_1587.htm#SEC1663 62398 2275 iostruct sing_1841.htm#SEC1917 60444 2276 irrRealizationDim sing_2127.htm#SEC2203 7814 2277 irred_secondary_char0 irred_secondary_char0 sing_1665.htm#SEC1741 2943 2278 irred_secondary_no_molien irred_secondary_no_molien sing_1668.htm#SEC1744 55905 2279 irreddecMon sing_1208.htm#SEC1284 20160 2280 irreducible power series sing_1569.htm#IDX764 2281 irreducible secondary invariant irred_secondary_char0 sing_1665.htm#IDX778 2282 isAface sing_2421.htm#SEC2497 25344 2285 2283 isAntiEndo sing_669.htm#SEC721 19156 2286 isBounded sing_209 6.htm#SEC2172281832284 isBounded sing_2098.htm#SEC2174 28183 2287 2285 isCI sing_209.htm#IDX139 58425 2288 isCI sing_11 29.htm#SEC12052286 isCI sing_1131.htm#SEC1207 2289 2287 isCM sing_209.htm#IDX140 50469 2290 isCM sing_11 69.htm#SEC12452291 isCMcod2 sing_162 0.htm#SEC169625632292 isCanonical sing_209 7.htm#SEC2173511092288 isCM sing_1171.htm#SEC1247 2289 isCMcod2 sing_1622.htm#SEC1698 2563 2290 isCanonical sing_2099.htm#SEC2175 51109 2293 2291 isCartan sing_531.htm#SEC583 39541 2294 2292 isCentral sing_740.htm#SEC792 54650 2295 2293 isCommutative sing_742.htm#SEC794 60728 2296 isCompatible sing_206 0.htm#SEC2136573232297 isCompressed sing_2 098.htm#SEC217428492298 isDenom sing_261 2.htm#SEC2688555372299 isEqualDivisor sing_23 54.htm#SEC2430175692300 isEquising sing_15 29.htm#SEC160514242301 isFlat sing_117 0.htm#SEC1246147062294 isCompatible sing_2062.htm#SEC2138 57323 2295 isCompressed sing_2100.htm#SEC2176 2849 2296 isDenom sing_2619.htm#SEC2695 55537 2297 isEqualDivisor sing_2360.htm#SEC2436 17569 2298 isEquising sing_1531.htm#SEC1607 1424 2299 isFlat sing_1172.htm#SEC1248 14706 2302 2300 isFsat sing_581.htm#SEC633 28225 2303 isFullSpace sing_203 6.htm#SEC2112274332304 isGorenstein sing_2 099.htm#SEC2175240102305 isGradedRingHomomorphism isGradedRingHomomorphism sing_25 53.htm#SEC2629395512306 isGroup sing_255 1.htm#SEC2627557442307 isGroupHomomorphism sing_255 2.htm#SEC2628654752301 isFullSpace sing_2038.htm#SEC2114 27433 2302 isGorenstein sing_2101.htm#SEC2177 24010 2303 isGradedRingHomomorphism isGradedRingHomomorphism sing_2560.htm#SEC2636 39551 2304 isGroup sing_2558.htm#SEC2634 55744 2305 isGroupHomomorphism sing_2559.htm#SEC2635 65475 2308 2306 isHolonomic sing_559.htm#SEC611 30274 2309 2307 isHomg sing_209.htm#IDX135 2310 isHomogeneous sing_25 79.htm#SEC265530342311 isInS sing_26 49.htm#SEC2725309072308 isHomogeneous sing_2586.htm#SEC2662 3034 2309 isInS sing_2656.htm#SEC2732 30907 2312 2310 isInt sing_594.htm#SEC646 9879 2313 isIntegralSurjective isIntegralSurjective sing_25 65.htm#SEC2641sprintf2314 isInvertibleLeftFraction isInvertibleLeftFraction sing_26 59.htm#SEC27356232315 isInvertibleNcfrac sing_26 07.htm#SEC2683483672311 isIntegralSurjective isIntegralSurjective sing_2572.htm#SEC2648 sprintf 2312 isInvertibleLeftFraction isInvertibleLeftFraction sing_2666.htm#SEC2742 623 2313 isInvertibleNcfrac sing_2614.htm#SEC2690 48367 2316 2314 isInvolution sing_668.htm#SEC720 13601 2317 isLatticeEmpty sing_210 0.htm#SEC2176485172318 isLocalizationRegular isLocalizationRegular sing_241 1.htm#SEC2487112212319 isLocallyFree sing_117 1.htm#SEC1247463892320 isMonomial sing_119 2.htm#SEC1268576152315 isLatticeEmpty sing_2102.htm#SEC2178 48517 2316 isLocalizationRegular isLocalizationRegular sing_2417.htm#SEC2493 11221 2317 isLocallyFree sing_1173.htm#SEC1249 46389 2318 isMonomial sing_1194.htm#SEC1270 57615 2321 2319 isNC sing_741.htm#SEC793 57151 2322 isNormal sing_210 1.htm#SEC2177642362323 isOnCurve sing_190 4.htm#SEC1980363242324 isOneFraction sing_266 2.htm#SEC2738550152325 isOneNcfrac sing_260 1.htm#SEC2677127542326 isOrigin sing_203 7.htm#SEC2113139772327 isPositive sing_25 76.htm#SEC2652508522328 isPrimitiveSublattice isPrimitiveSublattice sing_25 66.htm#SEC2642sprintf2329 isPure sing_206 1.htm#SEC2137440022320 isNormal sing_2103.htm#SEC2179 64236 2321 isOnCurve sing_1906.htm#SEC1982 36324 2322 isOneFraction sing_2669.htm#SEC2745 55015 2323 isOneNcfrac sing_2608.htm#SEC2684 12754 2324 isOrigin sing_2039.htm#SEC2115 13977 2325 isPositive sing_2583.htm#SEC2659 50852 2326 isPrimitiveSublattice isPrimitiveSublattice sing_2573.htm#SEC2649 sprintf 2327 isPure sing_2063.htm#SEC2139 44002 2330 2328 isPureTensor sing_503.htm#SEC555 21323 2331 isQuotientRing sing_102 4.htm#SEC1100sprintf2329 isQuotientRing sing_1026.htm#SEC1102 sprintf 2332 2330 isRational sing_562.htm#SEC614 57398 2333 isReflexive sing_210 2.htm#SEC217839912334 isReg sing_117 2.htm#SEC1248409202331 isReflexive sing_2104.htm#SEC2180 3991 2332 isReg sing_1174.htm#SEC1250 40920 2335 2333 isSB sing_209.htm#IDX134 2336 isSimplicial sing_20 38.htm#SEC2114577892337 isSmooth sing_210 3.htm#SEC2179376472338 isSubModule sing_102 5.htm#SEC1101sprintf2339 isSublattice sing_25 57.htm#SEC2633105012340 isSymmetric sing_134 1.htm#SEC1417613632341 isTame sing_155 4.htm#SEC1630319252342 isTerminal sing_210 4.htm#SEC2180294162343 isTorsionFree sing_25 75.htm#SEC2651522282334 isSimplicial sing_2040.htm#SEC2116 57789 2335 isSmooth sing_2105.htm#SEC2181 37647 2336 isSubModule sing_1027.htm#SEC1103 sprintf 2337 isSublattice sing_2564.htm#SEC2640 10501 2338 isSymmetric sing_1343.htm#SEC1419 61363 2339 isTame sing_1556.htm#SEC1632 31925 2340 isTerminal sing_2106.htm#SEC2182 29416 2341 isTorsionFree sing_2582.htm#SEC2658 52228 2344 2342 isTwoSidedGB sing_504.htm#SEC556 36558 2345 2343 isUpperTriangular sing_721.htm#SEC773 40655 2346 2344 isVar sing_660.htm#SEC712 43851 2347 isVeryAmple sing_210 5.htm#SEC2181646522345 isVeryAmple sing_2107.htm#SEC2183 64652 2348 2346 isWeyl sing_743.htm#SEC795 28994 2349 isZeroElement sing_25 77.htm#SEC26535142350 isZeroFraction sing_266 1.htm#SEC273719262351 isZeroNcfrac sing_260 0.htm#SEC267668412352 is_NND sing_157 0.htm#SEC1646265642353 is_NP sing_12 29.htm#SEC1305438912354 is_active sing_160 3.htm#SEC167968672355 is_bijective sing_111 6.htm#SEC1192495122347 isZeroElement sing_2584.htm#SEC2660 514 2348 isZeroFraction sing_2668.htm#SEC2744 1926 2349 isZeroNcfrac sing_2607.htm#SEC2683 6841 2350 is_NND sing_1572.htm#SEC1648 26564 2351 is_NP sing_1231.htm#SEC1307 43891 2352 is_active sing_1605.htm#SEC1681 6867 2353 is_bijective sing_1118.htm#SEC1194 49512 2356 2354 is_cenBimodule sing_776.htm#SEC828 35450 2357 2355 is_cenSubbimodule sing_777.htm#SEC829 26181 2358 is_ci sing_160 4.htm#SEC1680353702359 is_complex sing_105 2.htm#SEC112812342360 is_fix_injective sing_194 1.htm#SEC2017116632361 is_h_injective sing_194 0.htm#SEC2016366962362 is_injective sing_111 4.htm#SEC1190157762363 is_irred sing_156 7.htm#SEC1643511502364 is_is sing_160 5.htm#SEC1681641052365 is_nested sing_123 0.htm#SEC130692002366 is_prime sing_192 1.htm#SEC1997290182367 is_primitive_root sing_191 7.htm#SEC1993428382356 is_ci sing_1606.htm#SEC1682 35370 2357 is_complex sing_1054.htm#SEC1130 1234 2358 is_fix_injective sing_1943.htm#SEC2019 11663 2359 is_h_injective sing_1942.htm#SEC2018 36696 2360 is_injective sing_1116.htm#SEC1192 15776 2361 is_irred sing_1569.htm#SEC1645 51150 2362 is_is sing_1607.htm#SEC1683 64105 2363 is_nested sing_1232.htm#SEC1308 9200 2364 is_prime sing_1923.htm#SEC1999 29018 2365 is_primitive_root sing_1919.htm#SEC1995 42838 2368 2366 is_pure sing_768.htm#SEC820 59105 2369 is_reg sing_160 6.htm#SEC1682181462370 is_regs sing_160 7.htm#SEC1683502422371 is_surjective sing_111 5.htm#SEC1191570442372 is_zero sing_96 7.htm#SEC1043243412373 isartinianMon sing_120 3.htm#SEC127911032374 isgenericMon sing_120 4.htm#SEC1280144442375 ishyper sing_194 4.htm#SEC2020655182376 isirreducibleMon sing_120 2.htm#SEC1278224282377 isoncurve sing_194 5.htm#SEC2021163842378 isparam sing_20 08.htm#SEC2084563952379 isprimaryMon sing_120 1.htm#SEC1277573672380 isprimeMon sing_120 0.htm#SEC127691242381 isuni sing_199 3.htm#SEC2069394272367 is_reg sing_1608.htm#SEC1684 18146 2368 is_regs sing_1609.htm#SEC1685 50242 2369 is_surjective sing_1117.htm#SEC1193 57044 2370 is_zero sing_969.htm#SEC1045 24341 2371 isartinianMon sing_1205.htm#SEC1281 1103 2372 isgenericMon sing_1206.htm#SEC1282 14444 2373 ishyper sing_1946.htm#SEC2022 65518 2374 isirreducibleMon sing_1204.htm#SEC1280 22428 2375 isoncurve sing_1947.htm#SEC2023 16384 2376 isparam sing_2010.htm#SEC2086 56395 2377 isprimaryMon sing_1203.htm#SEC1279 57367 2378 isprimeMon sing_1202.htm#SEC1278 9124 2379 isuni sing_1995.htm#SEC2071 39427 2382 2380 iv2lp sing_629.htm#SEC681 59849 2383 2381 iv2lpList sing_630.htm#SEC682 18518 … … 2396 2394 ivSickleDim sing_619.htm#SEC671 64347 2397 2395 ivSickleHil sing_618.htm#SEC670 41396 2398 ivmatGaussian sing_268 0.htm#SEC2756377182399 ivmatInit sing_26 77.htm#SEC2753227742400 ivmatSet sing_26 78.htm#SEC2754534802401 jInvariant sing_213 7.htm#SEC221323692402 jOft sing_187 6.htm#SEC1952257162396 ivmatGaussian sing_2687.htm#SEC2763 37718 2397 ivmatInit sing_2684.htm#SEC2760 22774 2398 ivmatSet sing_2685.htm#SEC2761 53480 2399 jInvariant sing_2139.htm#SEC2215 2369 2400 jOft sing_1878.htm#SEC1954 25716 2403 2401 jacob sing_271.htm#SEC311 2404 jacoblift sing_158 6.htm#SEC1662401252405 jacobson sing_184 5.htm#SEC1921592672406 jacobson.lib sing_184 3.htm#SEC19192407 jacobson_lib sing_184 3.htm#SEC19192402 jacoblift sing_1588.htm#SEC1664 40125 2403 jacobson sing_1847.htm#SEC1923 59267 2404 jacobson.lib sing_1845.htm#SEC1921 2405 jacobson_lib sing_1845.htm#SEC1921 2408 2406 janet sing_272.htm#SEC312 2409 janet basis sing_26 86.htm#IDX10342407 janet basis sing_2693.htm#IDX1032 2410 2408 jet sing_273.htm#SEC313 2411 jordan sing_110 0.htm#SEC1176166022412 jordanbasis sing_110 1.htm#SEC1177127362413 jordanmatrix sing_110 2.htm#SEC117828862414 jordannf sing_110 3.htm#SEC1179205352415 jungfib sing_142 5.htm#SEC150154322416 jungnormal sing_142 4.htm#SEC1500435612417 jungresolve sing_142 3.htm#SEC1499450042418 katsura sing_96 5.htm#SEC1041459132409 jordan sing_1102.htm#SEC1178 16602 2410 jordanbasis sing_1103.htm#SEC1179 12736 2411 jordanmatrix sing_1104.htm#SEC1180 2886 2412 jordannf sing_1105.htm#SEC1181 20535 2413 jungfib sing_1427.htm#SEC1503 5432 2414 jungnormal sing_1426.htm#SEC1502 43561 2415 jungresolve sing_1425.htm#SEC1501 45004 2416 katsura sing_967.htm#SEC1043 45913 2419 2417 kbase sing_274.htm#SEC314 2420 2418 kbase (plural) sing_464.htm#SEC504 2421 2419 keepring sing_388.htm#SEC428 2422 kerHom sing_25 29.htm#SEC2605539062420 kerHom sing_2536.htm#SEC2612 53906 2423 2421 kernel sing_275.htm#SEC315 2424 kernelLattice sing_256 0.htm#SEC2636363202422 kernelLattice sing_2567.htm#SEC2643 36320 2425 2423 kill sing_276.htm#SEC316 2426 killTask sing_103 1.htm#SEC1107393172424 killTask sing_1033.htm#SEC1109 39317 2427 2425 killall sing_911.htm#SEC987 34661 2428 2426 killattrib sing_277.htm#SEC317 2429 2427 kmemory sing_910.htm#SEC986 52193 2430 kohom sing_117 4.htm#SEC1250500862431 kontrahom sing_117 5.htm#SEC1251585492428 kohom sing_1176.htm#SEC1252 50086 2429 kontrahom sing_1177.htm#SEC1253 58549 2432 2430 koszul sing_278.htm#SEC318 2433 kskernel.lib sing_157 7.htm#SEC16532434 kskernel_lib sing_157 7.htm#SEC16532431 kskernel.lib sing_1579.htm#SEC1655 2432 kskernel_lib sing_1579.htm#SEC1655 2435 2433 l-adic numbers sing_32.htm#SEC46 2436 2434 laguerre sing_279.htm#SEC319 2437 laguerre_solve sing_172 4.htm#SEC1800101552438 lastvarGeneral sing_197 4.htm#SEC2050286452439 latex.lib sing_17 68.htm#SEC18442440 latex_lib sing_17 68.htm#SEC18442441 lattice sing_22 09.htm#IDX9032442 latticeArea sing_208 0.htm#SEC2156537712443 latticeBasis sing_256 1.htm#SEC2637431622444 latticeCodegree sing_210 6.htm#SEC2182254822445 latticeDegree sing_210 7.htm#SEC2183528812446 latticePoints sing_21 08.htm#SEC2184419652447 latticeVolume sing_21 09.htm#SEC2185422342448 laxfrT sing_23 78.htm#SEC2454608992449 laxfrX sing_23 79.htm#SEC2455572542435 laguerre_solve sing_1726.htm#SEC1802 10155 2436 lastvarGeneral sing_1976.htm#SEC2052 28645 2437 latex.lib sing_1770.htm#SEC1846 2438 latex_lib sing_1770.htm#SEC1846 2439 lattice sing_2211.htm#IDX896 2440 latticeArea sing_2082.htm#SEC2158 53771 2441 latticeBasis sing_2568.htm#SEC2644 43162 2442 latticeCodegree sing_2108.htm#SEC2184 25482 2443 latticeDegree sing_2109.htm#SEC2185 52881 2444 latticePoints sing_2110.htm#SEC2186 41965 2445 latticeVolume sing_2111.htm#SEC2187 42234 2446 laxfrT sing_2384.htm#SEC2460 60899 2447 laxfrX sing_2385.htm#SEC2461 57254 2450 2448 lazy, option sing_315.htm#IDX156 2451 lcm sing_9 68.htm#SEC1044447552452 lcmMon sing_119 5.htm#SEC1271527492453 lcmN sing_188 5.htm#SEC1961523552454 lcmofall sing_140 5.htm#SEC1481568892449 lcm sing_970.htm#SEC1046 44755 2450 lcmMon sing_1197.htm#SEC1273 52749 2451 lcmN sing_1887.htm#SEC1963 52355 2452 lcmofall sing_1407.htm#SEC1483 56889 2455 2453 lead sing_280.htm#SEC320 2456 2454 leadcoef sing_281.htm#SEC321 2457 2455 leadexp sing_282.htm#SEC322 2458 2456 leadmonom sing_283.htm#SEC323 2459 leadmonomial sing_196 0.htm#SEC203681952457 leadmonomial sing_1962.htm#SEC2038 8195 2460 2458 left annihilator ideal sing_540.htm#IDX329 2461 leftInverse sing_183 4.htm#SEC1910414692462 leftKernel sing_183 2.htm#SEC190892922463 leftOre sing_265 2.htm#SEC2728446692464 length sing_26 75.htm#SEC275195472459 leftInverse sing_1836.htm#SEC1912 41469 2460 leftKernel sing_1834.htm#SEC1910 9292 2461 leftOre sing_2659.htm#SEC2735 44669 2462 length sing_2682.htm#SEC2758 9547 2465 2463 length, option sing_315.htm#IDX157 2466 2464 letplaceGBasis sing_646.htm#SEC698 33757 2467 2465 letterplace correspondence Letterplace correspondence sing_494.htm#SEC546 2468 lex_solve sing_173 0.htm#SEC1806486922466 lex_solve sing_1732.htm#SEC1808 48692 2469 2467 lexicographical ordering sing_860.htm#IDX390 2470 2468 lib2doc sing_60.htm#SEC97 2471 libSingular sing_27 54.htm#SEC28432469 libSingular sing_2761.htm#SEC2850 2472 2470 libcdd sing_1.htm#IDX12 2473 2471 libfac sing_1.htm#IDX6 2474 2472 libparse sing_69.htm#SEC109 2475 library sing_222 4.htm#IDX9182476 library, gitfan, GIT, geometric invariant theory, quotients gitfan_lib sing_24 14.htm#IDX9872473 library sing_2226.htm#IDX911 2474 library, gitfan, GIT, geometric invariant theory, quotients gitfan_lib sing_2420.htm#IDX984 2477 2475 library, info string sing_55.htm#IDX124 2478 library, polybori.lib sing_222 4.htm#IDX9152476 library, polybori.lib sing_2226.htm#IDX908 2479 2477 library, template sing_55.htm#SEC92 2480 2478 library, template.lib sing_55.htm#IDX122 … … 2483 2481 lift sing_498.htm#IDX305 2484 2482 lift (plural) sing_465.htm#SEC505 2485 lift_kbase sing_152 3.htm#SEC1599109062486 lift_rel_kb sing_152 4.htm#SEC1600136732483 lift_kbase sing_1525.htm#SEC1601 10906 2484 lift_rel_kb sing_1526.htm#SEC1602 13673 2487 2485 liftenvelope sing_501.htm#SEC553 58802 2488 2486 liftstd sing_286.htm#SEC326 … … 2491 2489 linReduceIdeal sing_514.htm#SEC566 19076 2492 2490 linSyzSolve sing_515.htm#SEC567 26185 2493 linalg.lib sing_10 78.htm#SEC11542494 linalg_lib sing_10 78.htm#SEC11542495 linealityDimension sing_20 39.htm#SEC2115307512496 linealitySpace sing_204 0.htm#SEC2116144892491 linalg.lib sing_1080.htm#SEC1156 2492 linalg_lib sing_1080.htm#SEC1156 2493 linealityDimension sing_2041.htm#SEC2117 30751 2494 linealitySpace sing_2042.htm#SEC2118 14489 2497 2495 linear algebra sing_210.htm#SEC250 2498 2496 linear algebra sing_289.htm#SEC329 2499 2497 linear algebra sing_290.htm#SEC330 2500 2498 linear algebra sing_291.htm#SEC331 2501 linear code, dual sing_180 3.htm#IDX7962502 linear code, systematic sing_180 4.htm#IDX7972499 linear code, dual sing_1805.htm#IDX789 2500 linear code, systematic sing_1806.htm#IDX790 2503 2501 linear interreduction sing_505.htm#IDX320 2504 2502 linearCombinations sing_534.htm#SEC586 20514 2505 2503 linearMapKernel sing_533.htm#SEC585 43761 2506 linear_relations sing_107 0.htm#SEC1146459832507 linearlyEquivalent sing_23 57.htm#SEC2433283512508 linearpart sing_171 6.htm#SEC179221622509 linesHypersurface sing_27 25.htm#SEC280191292504 linear_relations sing_1072.htm#SEC1148 45983 2505 linearlyEquivalent sing_2363.htm#SEC2439 28351 2506 linearpart sing_1718.htm#SEC1794 2162 2507 linesHypersurface sing_2732.htm#SEC2808 9129 2510 2508 link Parallelization with ssi links sing_113.htm#SEC153 2511 2509 link sing_815.htm#SEC867 … … 2518 2516 list operations sing_126.htm#SEC166 2519 2517 list related functions list related functions sing_127.htm#SEC167 2518 lists sing_2343.htm#IDX944 2519 lists, elements sing_2345.htm#IDX946 2520 2520 listvar sing_287.htm#SEC327 2521 lll sing_2 593.htm#SEC2669358272521 lll sing_2600.htm#SEC2676 35827 2522 2522 load sing_389.htm#SEC429 2523 2523 loadLib, option sing_315.htm#IDX178 2524 2524 loadProc, option sing_315.htm#IDX179 2525 locAtZero sing_125 0.htm#SEC132656872526 locNormal sing_118 4.htm#SEC1260522372527 locStatus sing_26 47.htm#SEC2723545752528 local methods sing_118 3.htm#IDX5562529 local methods sing_118 4.htm#IDX5592525 locAtZero sing_1252.htm#SEC1328 5687 2526 locNormal sing_1186.htm#SEC1262 52237 2527 locStatus sing_2654.htm#SEC2730 54575 2528 local methods sing_1185.htm#IDX549 2529 local methods sing_1186.htm#IDX552 2530 2530 local names sing_46.htm#SEC83 2531 2531 local rings, computing in Rings associated to monomial orderings sing_810.htm#SEC862 2532 2532 local weighted lexicographical ordering sing_861.htm#IDX411 2533 2533 local weighted reverse lexicographical ordering Local orderings sing_861.htm#IDX408 2534 localInvar sing_16 79.htm#SEC1755384782534 localInvar sing_1681.htm#SEC1757 38478 2535 2535 localization Rings associated to monomial orderings sing_810.htm#SEC862 2536 localization sing_21 89.htm#IDX8632536 localization sing_2191.htm#IDX856 2537 2537 localization of D-module sing_563.htm#IDX345 2538 2538 localization of D-module sing_780.htm#IDX383 2539 locally closed set sing_928.htm#IDX4 442540 locally closed set sing_929.htm#IDX4 462541 locally closed set sing_930.htm#IDX4 482542 locally closed set sing_931.htm#IDX4 522543 locally closed set sing_933.htm#IDX4 632544 localstd sing_197 0.htm#SEC2046255622545 locnormal.lib sing_118 3.htm#SEC12592546 locnormal_lib sing_118 3.htm#SEC12592547 locstd sing_16 08.htm#SEC1684258642539 locally closed set sing_928.htm#IDX435 2540 locally closed set sing_929.htm#IDX437 2541 locally closed set sing_930.htm#IDX439 2542 locally closed set sing_931.htm#IDX443 2543 locally closed set sing_933.htm#IDX453 2544 localstd sing_1972.htm#SEC2048 25562 2545 locnormal.lib sing_1185.htm#SEC1261 2546 locnormal_lib sing_1185.htm#SEC1261 2547 locstd sing_1610.htm#SEC1686 25864 2548 2548 locus FamElemsAtEnvCompPoints sing_935.htm#SEC1011 22530 2549 locus sing_935.htm#IDX4 682550 locus sing_936.htm#IDX4 712551 locus sing_937.htm#IDX4 742552 locus sing_938.htm#IDX4 772553 locus sing_939.htm#IDX4 802554 locus sing_940.htm#IDX4 822555 locus sing_941.htm#IDX4 862549 locus sing_935.htm#IDX458 2550 locus sing_936.htm#IDX461 2551 locus sing_937.htm#IDX464 2552 locus sing_938.htm#IDX467 2553 locus sing_939.htm#IDX470 2554 locus sing_940.htm#IDX472 2555 locus sing_941.htm#IDX476 2556 2556 locusdg sing_936.htm#SEC1012 6077 2557 2557 locusto sing_938.htm#SEC1014 730 2558 log2 sing_186 0.htm#SEC1936407032558 log2 sing_1862.htm#SEC1938 40703 2559 2559 logarithmic annihilator ideal sing_540.htm#IDX334 2560 logg sing_273 0.htm#SEC2806387362560 logg sing_2737.htm#SEC2813 38736 2561 2561 lp, global ordering sing_860.htm#IDX389 2562 2562 lp2iv sing_632.htm#SEC684 17398 … … 2587 2587 lpSickleHil sing_622.htm#SEC674 55268 2588 2588 lpSubstitute sing_641.htm#SEC693 54386 2589 lprint sing_94 6.htm#SEC102252852589 lprint sing_948.htm#SEC1024 5285 2590 2590 lres sing_288.htm#SEC328 2591 2591 ls, local ordering sing_861.htm#IDX402 2592 2592 lst2str sing_655.htm#SEC707 10088 2593 lsum sing_115 0.htm#SEC1226503152593 lsum sing_1152.htm#SEC1228 50315 2594 2594 ludecomp sing_289.htm#SEC329 2595 2595 luinverse sing_290.htm#SEC330 2596 2596 lusolve sing_291.htm#SEC331 2597 mRes sing_2 497.htm#SEC2573587022598 m_merkle_hellman_decryption m_merkle_hellman_decryption sing_193 2.htm#SEC2008579452599 m_merkle_hellman_encryption m_merkle_hellman_encryption sing_193 1.htm#SEC2007338572600 m_merkle_hellman_transformation m_merkle_hellman_transformation sing_193 0.htm#SEC200678802601 magnitude sing_185 4.htm#SEC1930379672602 makeDivisor sing_23 49.htm#SEC242534142603 makeFormalDivisor sing_23 59.htm#SEC2435545792604 makeGraph sing_114 1.htm#SEC1217217582605 makeGraphVE sing_27 16.htm#SEC2792sprintf2597 mRes sing_2504.htm#SEC2580 58702 2598 m_merkle_hellman_decryption m_merkle_hellman_decryption sing_1934.htm#SEC2010 57945 2599 m_merkle_hellman_encryption m_merkle_hellman_encryption sing_1933.htm#SEC2009 33857 2600 m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1932.htm#SEC2008 7880 2601 magnitude sing_1856.htm#SEC1932 37967 2602 makeDivisor sing_2355.htm#SEC2431 3414 2603 makeFormalDivisor sing_2365.htm#SEC2441 54579 2604 makeGraph sing_1143.htm#SEC1219 21758 2605 makeGraphVE sing_2723.htm#SEC2799 sprintf 2606 2606 makeHeisenberg sing_731.htm#SEC783 2050 2607 makeIdeal sing_24 89.htm#SEC2565578292607 makeIdeal sing_2496.htm#SEC2572 57829 2608 2608 makeLetterplaceRing sing_645.htm#SEC697 1592 2609 2609 makeMalgrange sing_600.htm#SEC652 41377 2610 makeMatrix sing_24 88.htm#SEC2564643482610 makeMatrix sing_2495.htm#SEC2571 64348 2611 2611 makeModElimRing sing_748.htm#SEC800 56092 2612 makePDivisor sing_23 65.htm#SEC2441452732612 makePDivisor sing_2371.htm#SEC2447 45273 2613 2613 makeQsl2 sing_695.htm#SEC747 3997 2614 2614 makeQsl3 sing_696.htm#SEC748 41249 2615 2615 makeQso3 sing_694.htm#SEC746 58910 2616 makeSheaf sing_27 04.htm#SEC2780104972616 makeSheaf sing_2711.htm#SEC2787 10497 2617 2617 makeUe6 sing_691.htm#SEC743 58585 2618 2618 makeUe7 sing_692.htm#SEC744 61849 … … 2636 2636 makeUsp4 sing_687.htm#SEC739 51690 2637 2637 makeUsp5 sing_688.htm#SEC740 35951 2638 makeVariety sing_2 696.htm#SEC2772239152639 makeVector sing_25 17.htm#SEC259390492638 makeVariety sing_2703.htm#SEC2779 23915 2639 makeVector sing_2524.htm#SEC2600 9049 2640 2640 makeWeyl sing_730.htm#SEC782 8554 2641 2641 map sing_128.htm#SEC168 … … 2649 2649 map related functions map related functions sing_132.htm#IDX131 2650 2650 map related functions (plural) map related functions (plural) sing_432.htm#IDX301 2651 mapIsFinite sing_11 18.htm#SEC1194608972652 mapToRatNormCurve sing_138 0.htm#SEC145688772653 mapall sing_101 1.htm#SEC1087149072654 mappingcone sing_24 76.htm#SEC2552482192655 mappingcone3 sing_24 78.htm#SEC2554589732656 markov4ti2 sing_133 6.htm#SEC141291632657 mat2arr sing_217 4.htm#SEC2250208402658 mat2carr sing_217 5.htm#SEC2251137772659 mat_rk sing_109 2.htm#SEC1168321962660 matbil sing_198 1.htm#SEC205716112651 mapIsFinite sing_1120.htm#SEC1196 60897 2652 mapToRatNormCurve sing_1382.htm#SEC1458 8877 2653 mapall sing_1013.htm#SEC1089 14907 2654 mappingcone sing_2482.htm#SEC2558 48219 2655 mappingcone3 sing_2484.htm#SEC2560 58973 2656 markov4ti2 sing_1338.htm#SEC1414 9163 2657 mat2arr sing_2176.htm#SEC2252 20840 2658 mat2carr sing_2177.htm#SEC2253 13777 2659 mat_rk sing_1094.htm#SEC1170 32196 2660 matbil sing_1983.htm#SEC2059 1611 2661 2661 mathematical objects Representation of mathematical objects sing_856.htm#SEC908 2662 mathinit sing_176 6.htm#SEC1842167932663 matmult sing_198 2.htm#SEC2058600882662 mathinit sing_1768.htm#SEC1844 16793 2663 matmult sing_1984.htm#SEC2060 60088 2664 2664 matrix sing_133.htm#SEC173 2665 matrix sing_217 4.htm#IDX8312666 matrix sing_217 5.htm#IDX8342667 matrix sing_217 6.htm#IDX8382665 matrix sing_2176.htm#IDX824 2666 matrix sing_2177.htm#IDX827 2667 matrix sing_2178.htm#IDX831 2668 2668 matrix declarations sing_134.htm#SEC174 2669 matrix diagonalization sing_184 3.htm#IDX8072669 matrix diagonalization sing_1845.htm#IDX800 2670 2670 matrix expressions sing_135.htm#SEC175 2671 2671 matrix operations sing_137.htm#SEC177 2672 2672 matrix related functions matrix related functions sing_138.htm#SEC178 2673 2673 matrix type cast sing_136.htm#SEC176 2674 matrix.lib sing_104 5.htm#SEC11212675 matrixExp sing_137 0.htm#SEC1446530632676 matrixLog sing_137 1.htm#SEC1447262352677 matrixT1 sing_162 2.htm#SEC1698150512678 matrix_lib sing_104 5.htm#SEC11212679 matrixpres sing_248 1.htm#SEC2557606452680 matrixsystem sing_23 89.htm#SEC2465629502674 matrix.lib sing_1047.htm#SEC1123 2675 matrixExp sing_1372.htm#SEC1448 53063 2676 matrixLog sing_1373.htm#SEC1449 26235 2677 matrixT1 sing_1624.htm#SEC1700 15051 2678 matrix_lib sing_1047.htm#SEC1123 2679 matrixpres sing_2487.htm#SEC2563 60645 2680 matrixsystem sing_2395.htm#SEC2471 62950 2681 2681 max sing_292.htm#SEC332 23624 2682 maxEord sing_139 5.htm#SEC1471640322682 maxEord sing_1397.htm#SEC1473 64032 2683 2683 maxExp sing_209.htm#IDX136 2684 2684 maxIntRoot sing_797.htm#SEC849 37127 2685 maxZeros sing_137 3.htm#SEC1449359642686 maxabs sing_200 0.htm#SEC2076645102687 maxcoef sing_9 69.htm#SEC1045505772688 maxdeg sing_97 0.htm#SEC1046397942689 maxdeg1 sing_97 1.htm#SEC1047215452685 maxZeros sing_1375.htm#SEC1451 35964 2686 maxabs sing_2002.htm#SEC2078 64510 2687 maxcoef sing_971.htm#SEC1047 50577 2688 maxdeg sing_972.htm#SEC1048 39794 2689 maxdeg1 sing_973.htm#SEC1049 21545 2690 2690 maxideal sing_293.htm#SEC333 2691 maximalFace sing_211 0.htm#SEC2186352242692 maximalGroebnerCone sing_216 4.htm#SEC2240629352693 maximalValue sing_211 1.htm#SEC2187327832694 maximum sing_187 3.htm#SEC194923552695 maximum number of zeroes sing_137 3.htm#IDX6142691 maximalFace sing_2112.htm#SEC2188 35224 2692 maximalGroebnerCone sing_2166.htm#SEC2242 62935 2693 maximalValue sing_2113.htm#SEC2189 32783 2694 maximum sing_1875.htm#SEC1951 2355 2695 maximum number of zeroes sing_1375.htm#IDX607 2696 2696 mdouble sing_56.htm#SEC93 56685 2697 2697 mem, option sing_315.htm#IDX180 2698 membershipMon sing_1196.htm#SEC1272 40876 2698 member sing_2345.htm#SEC2421 1765 2699 membershipMon sing_1198.htm#SEC1274 40876 2699 2700 memory sing_294.htm#SEC334 2700 2701 memory managment sing_294.htm#SEC334 2701 merkle_hellman_decryption merkle_hellman_decryption sing_1934.htm#SEC2010 49106 2702 merkle_hellman_encryption merkle_hellman_encryption sing_1933.htm#SEC2009 13645 2703 midpoint sing_2385.htm#SEC2461 29391 2704 milnor sing_1609.htm#SEC1685 23173 2705 milnorcode sing_1493.htm#SEC1569 13849 2706 milnornumber sing_2670.htm#SEC2746 21855 2702 merkle_hellman_decryption merkle_hellman_decryption sing_1936.htm#SEC2012 49106 2703 merkle_hellman_encryption merkle_hellman_encryption sing_1935.htm#SEC2011 13645 2704 methods, hashtables sing_2490.htm#IDX988 2705 methods.lib sing_2490.htm#SEC2566 2706 methods_lib sing_2490.htm#SEC2566 2707 midpoint sing_2391.htm#SEC2467 29391 2708 milnor sing_1611.htm#SEC1687 23173 2709 milnorcode sing_1495.htm#SEC1571 13849 2710 milnornumber sing_2677.htm#SEC2753 21855 2707 2711 min sing_295.htm#SEC335 56342 2708 minAssChar sing_129 5.htm#SEC1371187582709 minAssCharE sing_129 6.htm#SEC1372315702710 minAssGTZ sing_129 3.htm#SEC1369413152711 minAssGTZE sing_129 4.htm#SEC1370508672712 minAssZ sing_131 3.htm#SEC1389541522713 minEcart sing_196 3.htm#SEC2039348902712 minAssChar sing_1297.htm#SEC1373 18758 2713 minAssCharE sing_1298.htm#SEC1374 31570 2714 minAssGTZ sing_1295.htm#SEC1371 41315 2715 minAssGTZE sing_1296.htm#SEC1372 50867 2716 minAssZ sing_1315.htm#SEC1391 54152 2717 minEcart sing_1965.htm#SEC2041 34890 2714 2718 minIntRoot sing_561.htm#SEC613 3288 2715 2719 minIntRoot2 sing_796.htm#SEC848 46494 2716 minMult sing_112 5.htm#SEC1201319782720 minMult sing_1127.htm#SEC1203 31978 2717 2721 minbase sing_296.htm#SEC336 2718 minbaseMon sing_119 3.htm#SEC126915012719 mindeg sing_97 2.htm#SEC1048163072720 mindeg1 sing_97 3.htm#SEC1049396982721 mindist sing_18 18.htm#SEC1894552812722 minbaseMon sing_1195.htm#SEC1271 1501 2723 mindeg sing_974.htm#SEC1050 16307 2724 mindeg1 sing_975.htm#SEC1051 39698 2725 mindist sing_1820.htm#SEC1896 55281 2722 2726 minimal display time, setting the sing_358.htm#IDX284 2723 minimalAfaceOrbits sing_24 27.htm#SEC250324672724 minimalAfaces sing_24 18.htm#SEC2494477362725 minimalFace sing_211 2.htm#SEC2188409712726 minimalOrbitConeOrbits minimalOrbitConeOrbits sing_24 29.htm#SEC2505117562727 minimalValue sing_211 3.htm#SEC2189312622728 minipoly sing_109 7.htm#SEC117349272729 minkowskiSum sing_211 4.htm#SEC219039692727 minimalAfaceOrbits sing_2433.htm#SEC2509 2467 2728 minimalAfaces sing_2424.htm#SEC2500 47736 2729 minimalFace sing_2114.htm#SEC2190 40971 2730 minimalOrbitConeOrbits minimalOrbitConeOrbits sing_2435.htm#SEC2511 11756 2731 minimalValue sing_2115.htm#SEC2191 31262 2732 minipoly sing_1099.htm#SEC1175 4927 2733 minkowskiSum sing_2116.htm#SEC2192 3969 2730 2734 minor sing_297.htm#SEC337 2731 2735 minpoly sing_397.htm#SEC437 2732 2736 minres sing_298.htm#SEC338 2733 2737 minres (plural) sing_467.htm#SEC507 2734 mirror symmetry sing_114 0.htm#IDX5242735 mixed Hodge structure sing_153 1.htm#IDX6702736 mixed Hodge structure sing_153 7.htm#IDX6982737 mixed Hodge structure sing_15 38.htm#IDX7042738 mixed Hodge structure sing_15 39.htm#IDX7122739 mixed Hodge structure sing_154 0.htm#IDX7182740 mixed Hodge structure sing_154 1.htm#IDX7262741 mixed Hodge structure sing_154 2.htm#IDX7362742 mixed Hodge structure sing_155 3.htm#IDX7422743 mixed Hodge structure sing_155 5.htm#IDX7532738 mirror symmetry sing_1142.htm#IDX517 2739 mixed Hodge structure sing_1533.htm#IDX663 2740 mixed Hodge structure sing_1539.htm#IDX691 2741 mixed Hodge structure sing_1540.htm#IDX697 2742 mixed Hodge structure sing_1541.htm#IDX705 2743 mixed Hodge structure sing_1542.htm#IDX711 2744 mixed Hodge structure sing_1543.htm#IDX719 2745 mixed Hodge structure sing_1544.htm#IDX729 2746 mixed Hodge structure sing_1555.htm#IDX735 2747 mixed Hodge structure sing_1557.htm#IDX746 2744 2748 mod sing_81.htm#SEC121 2745 2749 mod sing_98.htm#SEC138 2746 2750 mod sing_147.htm#SEC187 2747 2751 mod sing_155.htm#SEC195 2748 mod2id sing_97 7.htm#SEC1053279272752 mod2id sing_979.htm#SEC1055 27927 2749 2753 mod2str sing_656.htm#SEC708 35236 2750 modBorder sing_26 88.htm#SEC2764192242751 modDec sing_121 2.htm#SEC1288485782752 modIntersect sing_119 0.htm#SEC1266436992753 modJanet sing_269 0.htm#SEC276685502754 modNPos sing_123 5.htm#SEC1311171302755 modNormal sing_118 6.htm#SEC1262396542756 modNpos_test sing_123 3.htm#SEC1309343262757 modSagbiAlg sing_233 0.htm#SEC2406250252758 modStd sing_11 88.htm#SEC126478242759 modSyz sing_11 89.htm#SEC1265370652760 modVStd sing_233 5.htm#SEC2411385292761 modVStd0 sing_233 6.htm#SEC2412460802762 modWalk sing_25 38.htm#SEC2614sprintf2763 mod_versal sing_152 2.htm#SEC1598639272764 modality sing_150 1.htm#SEC1577499512765 modfWalk sing_254 0.htm#SEC2616sprintf2766 modfrWalk sing_254 1.htm#SEC2617sprintf2767 modnormal.lib sing_118 5.htm#SEC12612768 modnormal_lib sing_118 5.htm#SEC12612769 modrWalk sing_25 39.htm#SEC2615sprintf2770 modregCM sing_12 39.htm#SEC131550492771 modsatiety sing_123 7.htm#SEC1313445062772 modstd.lib sing_118 7.htm#SEC12632773 modstd_lib sing_118 7.htm#SEC12632774 modular sing_95 5.htm#SEC1031169502775 modular methods sing_118 3.htm#IDX5572776 modular methods sing_118 5.htm#IDX5622777 modular methods. sing_118 4.htm#IDX5602778 modular techniques. sing_118 6.htm#IDX5642779 modular.lib sing_95 4.htm#SEC10302780 modular_lib sing_95 4.htm#SEC10302781 modular_lib sing_95 4.htm#IDX4922754 modBorder sing_2695.htm#SEC2771 19224 2755 modDec sing_1214.htm#SEC1290 48578 2756 modIntersect sing_1192.htm#SEC1268 43699 2757 modJanet sing_2697.htm#SEC2773 8550 2758 modNPos sing_1237.htm#SEC1313 17130 2759 modNormal sing_1188.htm#SEC1264 39654 2760 modNpos_test sing_1235.htm#SEC1311 34326 2761 modSagbiAlg sing_2332.htm#SEC2408 25025 2762 modStd sing_1190.htm#SEC1266 7824 2763 modSyz 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mp_res_mat sing_1729.htm#SEC1805 44453 2836 mplot sing_1769.htm#SEC1845 21740 2833 2837 mpresmat sing_302.htm#SEC342 2834 mprimdec.lib sing_12 08.htm#SEC12842835 mprimdec_lib sing_12 08.htm#SEC12842836 mregular.lib sing_122 3.htm#SEC12992837 mregular_lib sing_122 3.htm#SEC12992838 mprimdec.lib sing_1210.htm#SEC1286 2839 mprimdec_lib sing_1210.htm#SEC1286 2840 mregular.lib sing_1225.htm#SEC1301 2841 mregular_lib sing_1225.htm#SEC1301 2838 2842 mres sing_303.htm#SEC343 2839 2843 mres (plural) sing_469.htm#SEC509 … … 2845 2849 multBound sing_398.htm#SEC438 2846 2850 multRat sing_802.htm#SEC854 44047 2847 multarr2arr sing_220 5.htm#SEC2281447312848 multarrMultRestrict sing_220 7.htm#SEC2283417422849 multarrRestrict sing_220 6.htm#SEC2282sprintf2850 multcol sing_106 4.htm#SEC1140218992851 multdivisor sing_235 1.htm#SEC2427651392852 multformaldivisor sing_236 3.htm#SEC2439322382853 multi sing_19 48.htm#SEC2024184732851 multarr2arr sing_2207.htm#SEC2283 44731 2852 multarrMultRestrict 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nHilbertBasis sing_211 6.htm#SEC21921732889 nInteriorLatticePoints nInteriorLatticePoints sing_211 7.htm#SEC2193421522890 nLatticePoints sing_21 18.htm#SEC219459772891 naccache_stern_decryption naccache_stern_decryption sing_19 29.htm#SEC2005314292892 naccache_stern_encryption naccache_stern_encryption sing_19 28.htm#SEC2004600342893 naccache_stern_generation naccache_stern_generation sing_192 7.htm#SEC200325592859 multiDeg sing_2579.htm#SEC2655 7049 2860 multiDegBasis sing_2580.htm#SEC2656 3320 2861 multiDegGroebner sing_2588.htm#SEC2664 1040 2862 multiDegModulo sing_2590.htm#SEC2666 27244 2863 multiDegPartition sing_2581.htm#SEC2657 9577 2864 multiDegResolution sing_2591.htm#SEC2667 38535 2865 multiDegSyzygy sing_2589.htm#SEC2665 54075 2866 multiDegTensor sing_2592.htm#SEC2668 45108 2867 multiDegTor sing_2593.htm#SEC2669 sprintf 2868 multiarrangement sing_2203.htm#IDX877 2869 multiarrangement sing_2204.htm#IDX879 2870 multiarrangement sing_2205.htm#IDX882 2871 multiarrangement sing_2206.htm#IDX883 2872 multiarrangement sing_2207.htm#IDX886 2873 multiarrangement sing_2208.htm#IDX889 2874 multiarrangement sing_2209.htm#IDX891 2875 multidimensional_knapsack multidimensional_knapsack sing_1928.htm#SEC2004 15647 2876 multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2549.htm#IDX995 2877 multigrading.lib sing_2549.htm#IDX993 2878 multigrading_lib sing_2549.htm#IDX994 2879 multipleCover sing_2731.htm#SEC2807 55988 2880 multiplicities, sequence of sing_1564.htm#IDX761 2881 multiplicity sing_2348.htm#IDX953 2882 multiplicity sequence sing_1477.htm#IDX640 2883 multiplicity sequence sing_1480.htm#IDX652 2884 multiplicity sequence sing_1566.htm#IDX762 2885 multiplyLeftFractions multiplyLeftFractions sing_2664.htm#SEC2740 57489 2886 multiplylist sing_1417.htm#SEC1493 34999 2887 multivariate equations sing_1703.htm#IDX779 2888 multrow sing_1067.htm#SEC1143 871 2889 multseq2charexp sing_1476.htm#SEC1552 sprintf 2890 multsequence sing_1566.htm#SEC1642 35117 2891 nBoundaryLatticePoints nBoundaryLatticePoints sing_2117.htm#SEC2193 49670 2892 nHilbertBasis sing_2118.htm#SEC2194 173 2893 nInteriorLatticePoints nInteriorLatticePoints sing_2119.htm#SEC2195 42152 2894 nLatticePoints sing_2120.htm#SEC2196 5977 2895 naccache_stern_decryption naccache_stern_decryption sing_1931.htm#SEC2007 31429 2896 naccache_stern_encryption naccache_stern_encryption sing_1930.htm#SEC2006 60034 2897 naccache_stern_generation naccache_stern_generation sing_1929.htm#SEC2005 2559 2894 2898 nameof sing_306.htm#SEC346 2895 2899 names sing_307.htm#SEC347 2896 nashmult sing_148 2.htm#SEC155884912900 nashmult sing_1484.htm#SEC1560 8491 2897 2901 nblocks sing_358.htm#IDX221 2898 2902 ncExt_R sing_771.htm#SEC823 14357 2899 ncHilb.lib sing_2 594.htm#SEC26702900 ncHilb_lib sing_2 594.htm#SEC26702903 ncHilb.lib sing_2601.htm#SEC2677 2904 ncHilb_lib sing_2601.htm#SEC2677 2901 2905 ncHom sing_772.htm#SEC824 45033 2902 2906 ncRelations sing_739.htm#SEC791 7225 … … 2912 2916 ncfactor.lib sing_704.htm#SEC756 2913 2917 ncfactor_lib sing_704.htm#SEC756 2914 ncfrac.lib sing_2 597.htm#SEC26732915 ncfrac_lib sing_2 597.htm#SEC26732916 nchilb sing_2 595.htm#SEC2671405172918 ncfrac.lib sing_2604.htm#SEC2680 2919 ncfrac_lib sing_2604.htm#SEC2680 2920 nchilb sing_2602.htm#SEC2678 40517 2917 2921 nchomolog.lib sing_770.htm#IDX373 2918 2922 nchomolog_lib sing_770.htm#IDX374 2919 ncloc.lib sing_261 1.htm#SEC26872920 ncloc_lib sing_261 1.htm#SEC26872923 ncloc.lib sing_2618.htm#SEC2694 2924 ncloc_lib sing_2618.htm#SEC2694 2921 2925 ncols sing_308.htm#SEC348 2922 ncones sing_206 3.htm#SEC2139483162926 ncones sing_2065.htm#SEC2141 48316 2923 2927 ncpreim.lib sing_717.htm#SEC769 2924 2928 ncpreim_lib sing_717.htm#SEC769 … … 2926 2930 nctools_lib sing_725.htm#SEC777 2927 2931 ndcond sing_728.htm#SEC780 1006 2928 negateNcfrac sing_26 06.htm#SEC2682236262929 negatedCone sing_204 1.htm#SEC2117385272932 negateNcfrac 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netvectorShort sing_2646.htm#SEC2722 22053 2968 newTest sing_1870.htm#SEC1946 36655 2965 2969 newline sing_171.htm#SEC211 2966 news sing_27 47.htm#SEC28232970 news sing_2754.htm#SEC2830 2967 2971 newstruct sing_182.htm#SEC222 2968 newstruct sing_222 4.htm#IDX9202969 newtonDiag sing_98 1.htm#SEC1057566522970 newtonPolygonNegSlopes newtonPolygonNegSlopes sing_274 0.htm#SEC2816220522971 newtonPolytope sing_206 7.htm#SEC2143562912972 newtonPolytopeLP sing_207 2.htm#SEC2148361862973 newtonPolytopeP sing_207 1.htm#SEC2147299272974 newtonpoly sing_15 69.htm#SEC1645319302975 nf_icis sing_161 0.htm#SEC1686490932976 nfmodStd sing_26 43.htm#SEC2719460772977 nfmodSyz sing_26 45.htm#SEC2721559422978 nfmodstd.lib sing_264 1.htm#SEC27172979 nfmodstd_lib sing_264 1.htm#SEC27172980 nfmodsyz.lib sing_26 44.htm#SEC27202981 nfmodsyz_lib sing_26 44.htm#SEC27202982 nilpotent Lie algebras sing_13 68.htm#IDX5992983 nmaxcones sing_206 2.htm#SEC21386602972 newstruct sing_2226.htm#IDX913 2973 newtonDiag sing_983.htm#SEC1059 56652 2974 newtonPolygonNegSlopes newtonPolygonNegSlopes sing_2747.htm#SEC2823 22052 2975 newtonPolytope sing_2069.htm#SEC2145 56291 2976 newtonPolytopeLP sing_2074.htm#SEC2150 36186 2977 newtonPolytopeP sing_2073.htm#SEC2149 29927 2978 newtonpoly sing_1571.htm#SEC1647 31930 2979 nf_icis sing_1612.htm#SEC1688 49093 2980 nfmodStd sing_2650.htm#SEC2726 46077 2981 nfmodSyz sing_2652.htm#SEC2728 55942 2982 nfmodstd.lib sing_2648.htm#SEC2724 2983 nfmodstd_lib sing_2648.htm#SEC2724 2984 nfmodsyz.lib sing_2651.htm#SEC2727 2985 nfmodsyz_lib sing_2651.htm#SEC2727 2986 nilpotent Lie algebras sing_1370.htm#IDX592 2987 nmaxcones sing_2064.htm#SEC2140 660 2984 2988 noether sing_399.htm#SEC439 2985 noether.lib sing_123 1.htm#SEC13072986 noetherNormal sing_111 7.htm#SEC1193445222987 noether_lib sing_123 1.htm#SEC13072989 noether.lib sing_1233.htm#SEC1309 2990 noetherNormal sing_1119.htm#SEC1195 44522 2991 noether_lib sing_1233.htm#SEC1309 2988 2992 non-english special characters sing_407.htm#IDX286 2989 nonMonomials sing_128 4.htm#SEC1360163092990 nonZeroEntry sing_112 0.htm#SEC11969332993 nonMonomials sing_1286.htm#SEC1362 16309 2994 nonZeroEntry sing_1122.htm#SEC1198 933 2991 2995 none, option sing_315.htm#IDX150 2992 norTest sing_125 1.htm#SEC1327sprintf2993 norm sing_194 7.htm#SEC2023311432996 norTest sing_1253.htm#SEC1329 sprintf 2997 norm sing_1949.htm#SEC2025 31143 2994 2998 normaform (up to a bound) sing_358.htm#IDX246 2995 normal sing_124 1.htm#SEC1317610732996 normal bundle, graph, rational curves, mutiple covers, lines on normalBundle sing_27 23.htm#IDX10632999 normal sing_1243.htm#SEC1319 61073 3000 normal bundle, graph, rational curves, mutiple covers, lines on normalBundle sing_2730.htm#IDX1061 2997 3001 normal form sing_868.htm#IDX417 2998 normal.lib sing_124 0.htm#SEC13162999 normalBundle sing_27 23.htm#SEC2799sprintf3000 normalC sing_124 3.htm#SEC1319348423001 normalConductor sing_125 5.htm#SEC1331260853002 normalFan sing_21 19.htm#SEC2195392163003 normalForm sing_235 3.htm#SEC2429349623004 normalI sing_13 28.htm#SEC140475163005 normalP sing_124 2.htm#SEC1318365843006 normalToricRing sing_12 58.htm#SEC1334296383007 normalToricRingFromBinomials normalToricRingFromBinomials sing_12 59.htm#SEC133523013008 normal_lib sing_124 0.htm#SEC13163009 normalform sing_1 498.htm#SEC157455503010 normalform sing_23 29.htm#IDX9483002 normal.lib sing_1242.htm#SEC1318 3003 normalBundle sing_2730.htm#SEC2806 sprintf 3004 normalC sing_1245.htm#SEC1321 34842 3005 normalConductor sing_1257.htm#SEC1333 26085 3006 normalFan sing_2121.htm#SEC2197 39216 3007 normalForm sing_2359.htm#SEC2435 34962 3008 normalI sing_1330.htm#SEC1406 7516 3009 normalP sing_1244.htm#SEC1320 36584 3010 normalToricRing sing_1260.htm#SEC1336 29638 3011 normalToricRingFromBinomials normalToricRingFromBinomials sing_1261.htm#SEC1337 2301 3012 normal_lib sing_1242.htm#SEC1318 3013 normalform sing_1500.htm#SEC1576 5550 3014 normalform sing_2331.htm#IDX941 3011 3015 normaliz sing_1.htm#IDX14 18426 3012 normaliz sing_127 1.htm#SEC13473013 normaliz.lib sing_125 6.htm#SEC13323014 normaliz_lib sing_125 6.htm#SEC13323015 normalization sing_118 3.htm#IDX5553016 normalization sing_118 4.htm#IDX5583017 normalization sing_118 5.htm#IDX5613018 normalization sing_118 6.htm#IDX5633019 normalization sing_124 1.htm#IDX5673020 normalization sing_124 2.htm#IDX5703021 normalization sing_124 3.htm#IDX5733022 normalization sing_125 5.htm#IDX5793023 normalization sing_125 6.htm#IDX5813024 normalization sing_234 1.htm#IDX9543025 normalization. sing_118 0.htm#IDX5543026 normalization. sing_137 5.htm#IDX6213027 normalize sing_97 4.htm#SEC1050447883028 normalizeMonoidal sing_26 63.htm#SEC2739330713029 normalizeRational sing_26 64.htm#SEC2740551773016 normaliz sing_1273.htm#SEC1349 3017 normaliz.lib sing_1258.htm#SEC1334 3018 normaliz_lib sing_1258.htm#SEC1334 3019 normalization sing_1185.htm#IDX548 3020 normalization sing_1186.htm#IDX551 3021 normalization sing_1187.htm#IDX554 3022 normalization sing_1188.htm#IDX556 3023 normalization sing_1243.htm#IDX560 3024 normalization sing_1244.htm#IDX563 3025 normalization sing_1245.htm#IDX566 3026 normalization sing_1257.htm#IDX572 3027 normalization sing_1258.htm#IDX574 3028 normalization sing_2347.htm#IDX951 3029 normalization. sing_1182.htm#IDX547 3030 normalization. sing_1377.htm#IDX614 3031 normalize sing_976.htm#SEC1052 44788 3032 normalizeMonoidal sing_2670.htm#SEC2746 33071 3033 normalizeRational sing_2671.htm#SEC2747 55177 3030 3034 not sing_101.htm#SEC141 3031 3035 notBuckets, option sing_315.htm#IDX160 … … 3033 3037 notSugar, option sing_315.htm#IDX159 3034 3038 notWarnSB, option sing_315.htm#IDX181 3035 npar sing_185 3.htm#SEC192957533039 npar sing_1855.htm#SEC1931 5753 3036 3040 npars sing_309.htm#SEC349 3037 nrRootsDeterm sing_19 78.htm#SEC2054sprintf3038 nrRootsProbab sing_197 7.htm#SEC2053sprintf3041 nrRootsDeterm sing_1980.htm#SEC2056 sprintf 3042 nrRootsProbab sing_1979.htm#SEC2055 sprintf 3039 3043 nres sing_310.htm#SEC350 3040 3044 nres (plural) sing_472.htm#SEC512 3041 3045 nrows sing_311.htm#SEC351 3042 nrroots sing_200 7.htm#SEC2083548673043 nsatiety sing_123 6.htm#SEC1312533333044 nselect sing_113 6.htm#SEC1212340573045 nt_solve sing_174 2.htm#SEC1818330613046 ntsolve.lib sing_174 1.htm#SEC18173047 ntsolve_lib sing_174 1.htm#SEC18173046 nrroots sing_2009.htm#SEC2085 54867 3047 nsatiety sing_1238.htm#SEC1314 53333 3048 nselect sing_1138.htm#SEC1214 34057 3049 nt_solve sing_1744.htm#SEC1820 33061 3050 ntsolve.lib sing_1743.htm#SEC1819 3051 ntsolve_lib sing_1743.htm#SEC1819 3048 3052 number sing_144.htm#SEC184 3049 number sing_21 78.htm#IDX8443053 number sing_2180.htm#IDX837 3050 3054 number declarations sing_145.htm#SEC185 3051 3055 number expressions sing_146.htm#SEC186 3052 3056 number operations sing_147.htm#SEC187 3053 3057 number related functions number related functions sing_148.htm#SEC188 3054 numberOfConesOfDimension numberOfConesOfDimension sing_206 4.htm#SEC214059053058 numberOfConesOfDimension numberOfConesOfDimension sing_2066.htm#SEC2142 5905 3055 3059 number_e sing_912.htm#SEC988 59152 3056 3060 number_pi sing_913.htm#SEC989 15492 3057 numerAlg.lib sing_135 0.htm#IDX5883058 numerAlg_lib sing_135 0.htm#IDX5893059 numerAlg_lib sing_135 5.htm#IDX5983060 numerDecom.lib sing_135 5.htm#IDX5923061 numerDecom_lib sing_135 0.htm#IDX5913062 numerDecom_lib sing_135 5.htm#IDX5933061 numerAlg.lib sing_1352.htm#IDX581 3062 numerAlg_lib sing_1352.htm#IDX582 3063 numerAlg_lib sing_1357.htm#IDX591 3064 numerDecom.lib sing_1357.htm#IDX585 3065 numerDecom_lib sing_1352.htm#IDX584 3066 numerDecom_lib sing_1357.htm#IDX586 3063 3067 numerator sing_312.htm#SEC352 3064 numerical irreducible decomposition sing_135 5.htm#IDX5943068 numerical irreducible decomposition sing_1357.htm#IDX587 3065 3069 nvars sing_313.htm#SEC353 3066 olga.lib sing_26 46.htm#SEC27223067 olga_lib sing_26 46.htm#SEC27223068 oneDimBelongSemigroup oneDimBelongSemigroup sing_112 7.htm#SEC1203343993069 oneNcfrac sing_26 03.htm#SEC2679356543070 olga.lib sing_2653.htm#SEC2729 3071 olga_lib sing_2653.htm#SEC2729 3072 oneDimBelongSemigroup oneDimBelongSemigroup sing_1129.htm#SEC1205 34399 3073 oneNcfrac sing_2610.htm#SEC2686 35654 3070 3074 online help The online help system sing_16.htm#SEC22 3071 3075 open sing_314.htm#SEC354 3072 opentex sing_177 0.htm#SEC1846542363076 opentex sing_1772.htm#SEC1848 54236 3073 3077 operatorBM sing_547.htm#SEC599 54875 3074 3078 operatorModulo sing_548.htm#SEC600 26064 … … 3079 3083 option sing_315.htm#SEC355 3080 3084 option(warn) sing_70.htm#SEC110 3081 optionIsSet sing_101 7.htm#SEC1093573253085 optionIsSet sing_1019.htm#SEC1095 57325 3082 3086 or Evaluation of logical expressions sing_101.htm#SEC141 3083 3087 or sing_411.htm#SEC451 3084 orbit sing_13 68.htm#IDX6013085 orbit sing_13 69.htm#IDX6053086 orbit sing_137 2.htm#IDX6103087 orbit sing_137 3.htm#IDX6133088 orbitConeOrbits sing_24 28.htm#SEC2504609793089 orbitCones sing_24 19.htm#SEC2495605283090 orbit_variety sing_16 69.htm#SEC1745226653091 orbitparam.lib sing_13 68.htm#SEC14443092 orbitparam_lib sing_13 68.htm#SEC14443088 orbit sing_1370.htm#IDX594 3089 orbit sing_1371.htm#IDX598 3090 orbit sing_1374.htm#IDX603 3091 orbit sing_1375.htm#IDX606 3092 orbitConeOrbits sing_2434.htm#SEC2510 60979 3093 orbitCones sing_2425.htm#SEC2501 60528 3094 orbit_variety sing_1671.htm#SEC1747 22665 3095 orbitparam.lib sing_1370.htm#SEC1446 3096 orbitparam_lib sing_1370.htm#SEC1446 3093 3097 ord sing_316.htm#SEC356 3094 ord_test sing_101 2.htm#SEC1088365323095 order ideal, border basis sing_26 87.htm#IDX10353096 order ideal, border basis sing_26 88.htm#IDX10363098 ord_test sing_1014.htm#SEC1090 36532 3099 order ideal, border basis sing_2694.htm#IDX1033 3100 order ideal, border basis sing_2695.htm#IDX1034 3097 3101 orderings General definitions for orderings sing_859.htm#SEC911 3098 3102 orderings introduction Introduction to orderings sing_858.htm#SEC910 … … 3104 3108 orderings, product sing_864.htm#SEC916 3105 3109 ordstr sing_317.htm#SEC357 3106 origin sing_201 2.htm#SEC2088314083107 orthogonalize sing_108 3.htm#SEC1159637113108 outer sing_105 3.htm#SEC1129640483110 origin sing_2014.htm#SEC2090 31408 3111 orthogonalize sing_1085.htm#SEC1161 63711 3112 outer sing_1055.htm#SEC1131 64048 3109 3113 output sing_41.htm#SEC71 3110 3114 p-adic numbers sing_32.htm#SEC46 3111 pFactor sing_190 2.htm#SEC1978315043115 pFactor sing_1904.htm#SEC1980 31504 3112 3116 pIntersect sing_511.htm#SEC563 44055 3113 3117 pIntersectSyz sing_512.htm#SEC564 45608 … … 3115 3119 package declarations package declarations sing_150.htm#SEC190 3116 3120 package related functions package related functions sing_151.htm#SEC191 3117 pairset sing_196 7.htm#SEC2043382583121 pairset sing_1969.htm#SEC2045 38258 3118 3122 par sing_318.htm#SEC358 3119 3123 par2varRing sing_896.htm#SEC972 44769 3120 paraConic sing_138 3.htm#SEC145998283121 paraPlaneCurve sing_137 7.htm#SEC1453340943122 parallel skeletons sing_95 6.htm#IDX4983123 parallel.lib sing_95 6.htm#SEC10323124 parallelTestAND sing_96 0.htm#SEC103614153125 parallelTestOR sing_96 1.htm#SEC1037149203126 parallelWaitAll sing_9 59.htm#SEC103520173127 parallelWaitFirst sing_9 58.htm#SEC1034323128 parallelWaitN sing_95 7.htm#SEC1033388783129 parallel_lib sing_95 6.htm#SEC10323130 parallelization sing_95 6.htm#IDX4973131 parallelization sing_99 6.htm#IDX5003132 parallelization sing_10 29.htm#IDX5103133 param sing_156 0.htm#SEC1636572203124 paraConic sing_1385.htm#SEC1461 9828 3125 paraPlaneCurve sing_1379.htm#SEC1455 34094 3126 parallel skeletons sing_958.htm#IDX491 3127 parallel.lib sing_958.htm#SEC1034 3128 parallelTestAND sing_962.htm#SEC1038 1415 3129 parallelTestOR sing_963.htm#SEC1039 14920 3130 parallelWaitAll sing_961.htm#SEC1037 2017 3131 parallelWaitFirst sing_960.htm#SEC1036 32 3132 parallelWaitN sing_959.htm#SEC1035 38878 3133 parallel_lib sing_958.htm#SEC1034 3134 parallelization sing_958.htm#IDX490 3135 parallelization sing_998.htm#IDX493 3136 parallelization sing_1031.htm#IDX503 3137 param sing_1562.htm#SEC1638 57220 3134 3138 parameter, as numbers sing_144.htm#SEC184 3135 parameterSubstitute sing_21 59.htm#SEC2235631473139 parameterSubstitute sing_2161.htm#SEC2237 63147 3136 3140 parametric annihilator sing_540.htm#IDX335 3137 3141 parametric annihilator for variety sing_596.htm#IDX358 3138 parametric ideal sing_924.htm#IDX4 323139 parametric ideal sing_931.htm#IDX4 513140 parametric ideal sing_931.htm#IDX4 533141 parametric ideal sing_932.htm#IDX4 583142 parametrization sing_13 68.htm#IDX6023143 parametrization sing_137 2.htm#IDX6113144 parametrization sing_156 0.htm#IDX7633145 parametrizeOrbit sing_137 2.htm#SEC1448269693146 paraplanecurves.lib sing_137 4.htm#SEC14503147 paraplanecurves_lib sing_137 4.htm#SEC14503142 parametric ideal sing_924.htm#IDX423 3143 parametric ideal sing_931.htm#IDX442 3144 parametric ideal sing_931.htm#IDX444 3145 parametric ideal sing_932.htm#IDX449 3146 parametrization sing_1370.htm#IDX595 3147 parametrization sing_1374.htm#IDX604 3148 parametrization sing_1562.htm#IDX756 3149 parametrizeOrbit sing_1374.htm#SEC1450 26969 3150 paraplanecurves.lib sing_1376.htm#SEC1452 3151 paraplanecurves_lib sing_1376.htm#SEC1452 3148 3152 pardeg sing_319.htm#SEC359 3149 3153 parstr sing_320.htm#SEC360 3150 part sing_230 5.htm#SEC2381314853151 partOver sing_23 08.htm#SEC2384255553152 partUnder sing_23 09.htm#SEC2385131233153 partial_molien sing_164 7.htm#SEC1723217723154 partitions sing_11 48.htm#SEC1224480893155 partitions sing_11 48.htm#IDX5433156 path integral sing_114 0.htm#IDX5303157 pause sing_95 3.htm#SEC102922733154 part sing_2307.htm#SEC2383 31485 3155 partOver sing_2310.htm#SEC2386 25555 3156 partUnder sing_2311.htm#SEC2387 13123 3157 partial_molien sing_1649.htm#SEC1725 21772 3158 partitions sing_1150.htm#SEC1226 48089 3159 partitions sing_1150.htm#IDX536 3160 path integral sing_1142.htm#IDX523 3161 pause sing_955.htm#SEC1031 2273 3158 3162 pdivi sing_926.htm#SEC1002 21786 3159 pdivi sing_927.htm#IDX442 3160 pdivisorplus sing_2367.htm#SEC2443 47486 3161 permcol sing_1066.htm#SEC1142 12886 3162 permrow sing_1067.htm#SEC1143 26561 3163 permutationFromIntvec permutationFromIntvec sing_2434.htm#SEC2510 6533 3164 permutationToIntvec sing_2435.htm#SEC2511 1989 3165 permutations sing_1149.htm#IDX544 3166 permute sing_1149.htm#SEC1225 40893 3167 permute_L sing_1805.htm#SEC1881 10716 3163 pdivi sing_927.htm#IDX433 3164 pdivisorplus sing_2373.htm#SEC2449 47486 3165 permcol sing_1068.htm#SEC1144 12886 3166 permrow sing_1069.htm#SEC1145 26561 3167 permutationFromIntvec permutationFromIntvec sing_2440.htm#SEC2516 6533 3168 permutationToIntvec sing_2441.htm#SEC2517 1989 3169 permutations sing_1151.htm#IDX537 3170 permutations, sum, max, min sing_2342.htm#IDX943 3171 permute sing_1151.htm#SEC1227 40893 3172 permute_L sing_1807.htm#SEC1883 10716 3168 3173 perron sing_751.htm#SEC803 3782 3169 3174 perron.lib sing_750.htm#SEC802 3170 3175 perron_lib sing_750.htm#SEC802 3171 phindex.lib sing_22 19.htm#IDX9113172 phindex_lib sing_22 19.htm#IDX9123173 picksFormula sing_208 1.htm#SEC2157146563176 phindex.lib sing_2221.htm#IDX904 3177 phindex_lib sing_2221.htm#IDX905 3178 picksFormula sing_2083.htm#SEC2159 14656 3174 3179 pid sing_358.htm#IDX240 3175 plainInvariants sing_15 19.htm#SEC1595409163176 planeCur sing_232 7.htm#SEC2403sprintf3177 plot sing_178 3.htm#SEC1859466103178 plotRot sing_178 7.htm#SEC1863571503179 plotRotated sing_178 6.htm#SEC1862330093180 plotRotatedDirect sing_17 89.htm#SEC1865182023181 plotRotatedList sing_17 88.htm#SEC1864416683182 plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_179 0.htm#SEC1866388563183 plural sing_10 19.htm#IDX5053184 pmat sing_94 7.htm#SEC102338573180 plainInvariants sing_1521.htm#SEC1597 40916 3181 planeCur sing_2329.htm#SEC2405 sprintf 3182 plot sing_1785.htm#SEC1861 46610 3183 plotRot sing_1789.htm#SEC1865 57150 3184 plotRotated sing_1788.htm#SEC1864 33009 3185 plotRotatedDirect sing_1791.htm#SEC1867 18202 3186 plotRotatedList sing_1790.htm#SEC1866 41668 3187 plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1792.htm#SEC1868 38856 3188 plural sing_1021.htm#IDX498 3189 pmat sing_949.htm#SEC1025 3857 3185 3190 pnormalf sing_927.htm#SEC1003 26174 3186 pointid.lib sing_128 3.htm#SEC13593187 pointid_lib sing_128 3.htm#SEC13593191 pointid.lib sing_1285.htm#SEC1361 3192 pointid_lib sing_1285.htm#SEC1361 3188 3193 polSol sing_786.htm#SEC838 323 3189 3194 polSolFiniteRank sing_787.htm#SEC839 30875 3190 pollTask sing_10 39.htm#SEC1115539503195 pollTask sing_1041.htm#SEC1117 53950 3191 3196 poly sing_152.htm#SEC192 3192 3197 poly (plural) sing_438.htm#SEC478 … … 3199 3204 poly related functions poly related functions sing_156.htm#SEC196 3200 3205 poly related functions (plural) poly related functions (plural) sing_442.htm#SEC482 3201 poly.lib sing_96 2.htm#SEC10383206 poly.lib sing_964.htm#SEC1040 3202 3207 poly2list sing_589.htm#SEC641 4960 3203 poly2zdd sing_224 0.htm#SEC2316618393204 polyInterpolation sing_237 0.htm#SEC2446458663208 poly2zdd sing_2242.htm#SEC2318 61839 3209 polyInterpolation sing_2376.htm#SEC2452 45866 3205 3210 polyVars sing_793.htm#SEC845 43882 3206 poly_lib sing_96 2.htm#SEC10383207 polybori sing_222 4.htm#IDX9163208 polybori.lib sing_222 4.htm#IDX9133209 polybori.lib sing_222 4.htm#IDX9173210 polybori_lib sing_222 4.htm#IDX9143211 polymake sing_20 69.htm#IDX8173212 polymake.lib sing_20 69.htm#SEC21453213 polymakePolytope sing_207 0.htm#SEC2146473023214 polymake_lib sing_20 69.htm#SEC21453211 poly_lib sing_964.htm#SEC1040 3212 polybori sing_2226.htm#IDX909 3213 polybori.lib sing_2226.htm#IDX906 3214 polybori.lib sing_2226.htm#IDX910 3215 polybori_lib sing_2226.htm#IDX907 3216 polymake sing_2071.htm#IDX810 3217 polymake.lib sing_2071.htm#SEC2147 3218 polymakePolytope sing_2072.htm#SEC2148 47302 3219 polymake_lib sing_2071.htm#SEC2147 3215 3220 polynomial solutions sing_780.htm#IDX386 3216 3221 polynomial, opposite sing_358.htm#IDX232 3217 3222 polytope sing_190.htm#SEC230 3218 polytope sing_2069.htm#IDX813 3219 polytopeViaInequalities polytopeViaInequalities sing_2042.htm#SEC2118 52084 3220 polytopeViaPoints sing_2043.htm#SEC2119 281 3221 pos_def sing_1094.htm#SEC1170 4994 3222 poset sing_2209.htm#IDX902 3223 positiveOrthant sing_2013.htm#SEC2089 42102 3224 posweight sing_1627.htm#SEC1703 3364 3225 powSumSym sing_2262.htm#SEC2338 2339 3226 power sing_1054.htm#SEC1130 23365 3227 powerN sing_1886.htm#SEC1962 20170 3228 powerX sing_1895.htm#SEC1971 47971 3229 power_products sing_1661.htm#SEC1737 54629 3230 powerpolyX sing_1865.htm#SEC1941 37247 3231 powersums sing_1988.htm#SEC2064 59049 3232 preComp sing_1219.htm#SEC1295 16160 3223 polytope sing_2071.htm#IDX806 3224 polytopeViaInequalities polytopeViaInequalities sing_2044.htm#SEC2120 52084 3225 polytopeViaPoints sing_2045.htm#SEC2121 281 3226 pos_def sing_1096.htm#SEC1172 4994 3227 poset sing_2211.htm#IDX895 3228 positiveOrthant sing_2015.htm#SEC2091 42102 3229 posweight sing_1629.htm#SEC1705 3364 3230 powSumSym sing_2264.htm#SEC2340 2339 3231 power sing_1056.htm#SEC1132 23365 3232 power set sing_2344.htm#IDX945 3233 powerN sing_1888.htm#SEC1964 20170 3234 powerX sing_1897.htm#SEC1973 47971 3235 power_products sing_1663.htm#SEC1739 54629 3236 powerpolyX sing_1867.htm#SEC1943 37247 3237 powersums sing_1990.htm#SEC2066 59049 3238 preComp sing_1221.htm#SEC1297 16160 3233 3239 preimage sing_321.htm#SEC361 3234 3240 preimage sing_717.htm#IDX361 3235 3241 preimage (plural) sing_475.htm#SEC515 3236 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_101 5.htm#IDX5033237 preimageLattice sing_256 2.htm#SEC2638373483238 preimageLoc sing_101 5.htm#SEC1091333153242 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_1017.htm#IDX496 3243 preimageLattice sing_2569.htm#SEC2645 37348 3244 preimageLoc sing_1017.htm#SEC1093 33315 3239 3245 preimageNC sing_719.htm#SEC771 16037 3240 prepEmbDiv sing_144 5.htm#SEC1521367083241 prepMat sing_1 698.htm#SEC1774398683242 prepRealclassify sing_150 3.htm#SEC1579109943243 prepSV sing_180 0.htm#SEC1876500953244 prepareAss sing_130 2.htm#SEC1378218023245 presentTree sing_143 2.htm#SEC1508107313246 presentation sing_252 0.htm#SEC2596403233247 presolve.lib sing_17 08.htm#SEC17843248 presolve_lib sing_17 08.htm#SEC17843249 primL sing_189 0.htm#SEC1966145133250 primList sing_18 89.htm#SEC196568023251 primRoot sing_134 2.htm#SEC1418142103252 primTest sing_12 18.htm#SEC129481053253 primary decomposition sing_128 7.htm#IDX5833254 primary decomposition sing_131 0.htm#IDX5843255 primary decomposition of modules sing_12 08.htm#IDX5653256 primary decomposition, numerical sing_135 5.htm#IDX5963257 primary_char0 sing_165 1.htm#SEC1727614133258 primary_char0_no_molien primary_char0_no_molien sing_165 3.htm#SEC1729504773259 primary_char0_no_molien_random primary_char0_no_molien_random sing_16 58.htm#SEC173484223260 primary_char0_random primary_char0_random sing_165 6.htm#SEC173259963261 primary_charp sing_165 2.htm#SEC1728378633262 primary_charp_no_molien primary_charp_no_molien sing_165 4.htm#SEC1730322823263 primary_charp_no_molien_random primary_charp_no_molien_random sing_16 59.htm#SEC1735114983264 primary_charp_random primary_charp_random sing_165 7.htm#SEC1733247393265 primary_charp_without primary_charp_without sing_165 5.htm#SEC1731495853266 primary_charp_without_random primary_charp_without_random sing_166 0.htm#SEC1736369983267 primary_invariants sing_16 39.htm#SEC171555003268 primary_invariants_random primary_invariants_random sing_164 0.htm#SEC1716289583269 primdec.lib sing_128 7.htm#SEC13633270 primdecGTZ sing_12 89.htm#SEC136560913271 primdecGTZE sing_129 0.htm#SEC1366648823272 primdecMon sing_120 7.htm#SEC128338563273 primdecSY sing_129 1.htm#SEC136765473274 primdecSYE sing_129 2.htm#SEC1368527883275 primdecZ sing_131 1.htm#SEC1387481943276 primdecZM sing_131 2.htm#SEC1388172143277 primdec_lib sing_128 7.htm#SEC13633278 primdecint.lib sing_131 0.htm#SEC13863279 primdecint_lib sing_131 0.htm#SEC13863246 prepEmbDiv sing_1447.htm#SEC1523 36708 3247 prepMat sing_1700.htm#SEC1776 39868 3248 prepRealclassify sing_1505.htm#SEC1581 10994 3249 prepSV sing_1802.htm#SEC1878 50095 3250 prepareAss sing_1304.htm#SEC1380 21802 3251 presentTree sing_1434.htm#SEC1510 10731 3252 presentation sing_2527.htm#SEC2603 40323 3253 presolve.lib sing_1710.htm#SEC1786 3254 presolve_lib sing_1710.htm#SEC1786 3255 primL sing_1892.htm#SEC1968 14513 3256 primList sing_1891.htm#SEC1967 6802 3257 primRoot sing_1344.htm#SEC1420 14210 3258 primTest sing_1220.htm#SEC1296 8105 3259 primary decomposition sing_1289.htm#IDX576 3260 primary decomposition sing_1312.htm#IDX577 3261 primary decomposition of modules sing_1210.htm#IDX558 3262 primary decomposition, numerical sing_1357.htm#IDX589 3263 primary_char0 sing_1653.htm#SEC1729 61413 3264 primary_char0_no_molien primary_char0_no_molien sing_1655.htm#SEC1731 50477 3265 primary_char0_no_molien_random primary_char0_no_molien_random sing_1660.htm#SEC1736 8422 3266 primary_char0_random primary_char0_random sing_1658.htm#SEC1734 5996 3267 primary_charp sing_1654.htm#SEC1730 37863 3268 primary_charp_no_molien primary_charp_no_molien sing_1656.htm#SEC1732 32282 3269 primary_charp_no_molien_random primary_charp_no_molien_random sing_1661.htm#SEC1737 11498 3270 primary_charp_random primary_charp_random sing_1659.htm#SEC1735 24739 3271 primary_charp_without primary_charp_without sing_1657.htm#SEC1733 49585 3272 primary_charp_without_random primary_charp_without_random sing_1662.htm#SEC1738 36998 3273 primary_invariants sing_1641.htm#SEC1717 5500 3274 primary_invariants_random primary_invariants_random sing_1642.htm#SEC1718 28958 3275 primdec.lib sing_1289.htm#SEC1365 3276 primdecGTZ sing_1291.htm#SEC1367 6091 3277 primdecGTZE sing_1292.htm#SEC1368 64882 3278 primdecMon sing_1209.htm#SEC1285 3856 3279 primdecSY sing_1293.htm#SEC1369 6547 3280 primdecSYE sing_1294.htm#SEC1370 52788 3281 primdecZ sing_1313.htm#SEC1389 48194 3282 primdecZM sing_1314.htm#SEC1390 17214 3283 primdec_lib sing_1289.htm#SEC1365 3284 primdecint.lib sing_1312.htm#SEC1388 3285 primdecint_lib sing_1312.htm#SEC1388 3280 3286 prime sing_322.htm#SEC362 3281 primeClosure sing_124 6.htm#SEC1322435893287 primeClosure sing_1248.htm#SEC1324 43589 3282 3288 primecoeffs sing_919.htm#SEC995 46153 3283 3289 primefactors sing_323.htm#SEC363 3284 3290 primes sing_914.htm#SEC990 24408 3285 primitiv.lib sing_13 18.htm#SEC13943286 primitiv_lib sing_13 18.htm#SEC13943287 primitive sing_13 19.htm#SEC1395361633288 primitive element sing_13 19.htm#IDX5853289 primitiveSpan sing_25 69.htm#SEC2645sprintf3290 primitive_extra sing_132 0.htm#SEC1396490253291 primparam sing_151 4.htm#SEC1590353573291 primitiv.lib sing_1320.htm#SEC1396 3292 primitiv_lib sing_1320.htm#SEC1396 3293 primitive sing_1321.htm#SEC1397 36163 3294 primitive element sing_1321.htm#IDX578 3295 primitiveSpan sing_2576.htm#SEC2652 sprintf 3296 primitive_extra sing_1322.htm#SEC1398 49025 3297 primparam sing_1516.htm#SEC1592 35357 3292 3298 principal intersection sing_505.htm#IDX319 3293 3299 print sing_324.htm#SEC364 3294 print sing_217 6.htm#IDX8373295 printBetti sing_250 1.htm#SEC2577289413296 printFreeModule sing_2 493.htm#SEC2569133163297 printGraph sing_114 2.htm#SEC1218450413298 printGraphG sing_27 17.htm#SEC2793487423299 printGroup sing_255 0.htm#SEC262667913300 printHom sing_2 496.htm#SEC257270703301 printMatrix sing_249 2.htm#SEC2568155223302 printModule sing_2 495.htm#SEC2571sprintf3303 printMoebius sing_221 5.htm#SEC2291458283304 printResolution sing_2 494.htm#SEC2570292783305 printSheaf sing_27 05.htm#SEC2781317623306 printStack sing_27 19.htm#SEC279536923307 printTask sing_103 4.htm#SEC1110545493308 printVariety sing_2 697.htm#SEC277328463300 print sing_2178.htm#IDX830 3301 printBetti sing_2508.htm#SEC2584 28941 3302 printFreeModule sing_2500.htm#SEC2576 13316 3303 printGraph sing_1144.htm#SEC1220 45041 3304 printGraphG sing_2724.htm#SEC2800 48742 3305 printGroup sing_2557.htm#SEC2633 6791 3306 printHom sing_2503.htm#SEC2579 7070 3307 printMatrix sing_2499.htm#SEC2575 15522 3308 printModule sing_2502.htm#SEC2578 sprintf 3309 printMoebius sing_2217.htm#SEC2293 45828 3310 printResolution sing_2501.htm#SEC2577 29278 3311 printSheaf sing_2712.htm#SEC2788 31762 3312 printStack sing_2726.htm#SEC2802 3692 3313 printTask sing_1036.htm#SEC1112 54549 3314 printVariety sing_2704.htm#SEC2780 2846 3309 3315 printf sing_325.htm#SEC365 2294 3310 3316 printlevel sing_400.htm#SEC440 … … 3318 3324 procedures, static Procedure definition sing_43.htm#SEC78 3319 3325 procs with different argument types procs with different argument types sing_160.htm#SEC200 3320 prodcrit sing_196 5.htm#SEC2041562313326 prodcrit sing_1967.htm#SEC2043 56231 3321 3327 product sing_915.htm#SEC991 54431 3322 product variety, abstract variety sing_2 698.htm#IDX10513323 productVariety sing_2 698.htm#SEC2774541913324 productgroup sing_257 1.htm#SEC2647559373328 product variety, abstract variety sing_2705.htm#IDX1049 3329 productVariety sing_2705.htm#SEC2781 54191 3330 productgroup sing_2578.htm#SEC2654 55937 3325 3331 progress watch sing_315.htm#IDX163 3326 projectLattice sing_25 63.htm#SEC2639284633327 projective bundle, abstract variety, sheaf, enumeration of conics projectiveBundle sing_270 2.htm#IDX10553332 projectLattice sing_2570.htm#SEC2646 28463 3333 projective bundle, abstract variety, sheaf, enumeration of conics projectiveBundle sing_2709.htm#IDX1053 3328 3334 projective dimension purityfiltration_lib sing_758.htm#IDX370 3329 3335 projective limes sing_32.htm#SEC46 3330 projective space, abstract variety sing_270 1.htm#IDX10543331 projectiveBundle sing_270 2.htm#SEC2778137913336 projective space, abstract variety sing_2708.htm#IDX1052 3337 projectiveBundle sing_2709.htm#SEC2785 13791 3332 3338 projectiveDimension sing_759.htm#SEC811 8165 3333 projectiveSpace sing_270 1.htm#SEC2777217293339 projectiveSpace sing_2708.htm#SEC2784 21729 3334 3340 prompt sing_15.htm#SEC21 3335 3341 prompt, option sing_315.htm#IDX182 3336 propagator sing_114 0.htm#IDX528424603337 propagator sing_114 3.htm#SEC12193342 propagator sing_1142.htm#IDX521 42460 3343 propagator sing_1145.htm#SEC1221 3338 3344 prot, option sing_315.htm#IDX161 3339 3345 protocol of computations sing_315.htm#IDX162 3340 proximitymatrix sing_147 3.htm#SEC1549584033346 proximitymatrix sing_1475.htm#SEC1551 58403 3341 3347 prune sing_326.htm#SEC366 3342 pruneModule sing_25 27.htm#SEC2603514533343 prwalk sing_269 2.htm#SEC2768469633344 psigncnd sing_176 1.htm#SEC1837577343345 puiseux2generators sing_157 2.htm#SEC1648645083346 puiseuxExpansion sing_213 0.htm#SEC2206462773348 pruneModule sing_2534.htm#SEC2610 51453 3349 prwalk sing_2699.htm#SEC2775 46963 3350 psigncnd sing_1763.htm#SEC1839 57734 3351 puiseux2generators sing_1574.htm#SEC1650 64508 3352 puiseuxExpansion sing_2132.htm#SEC2208 46277 3347 3353 pure tensor sing_498.htm#IDX307 3348 3354 purelist sing_769.htm#SEC821 15517 … … 3352 3358 purityfiltration.lib purityfiltration_lib sing_758.htm#IDX365 3353 3359 purityfiltration_lib purityfiltration_lib sing_758.htm#IDX366 3354 pushForward sing_25 88.htm#SEC2664266973355 pwalk sing_115 6.htm#SEC1232611873360 pushForward sing_2595.htm#SEC2671 26697 3361 pwalk sing_1158.htm#SEC1234 61187 3356 3362 pyobject sing_191.htm#SEC231 3357 pyobject sing_222 4.htm#IDX9193363 pyobject sing_2226.htm#IDX912 3358 3364 pyobject declarations pyobject declarations sing_192.htm#SEC232 3359 3365 pyobject expressions pyobject expressions sing_193.htm#SEC233 3360 3366 pyobject operations sing_194.htm#SEC234 3361 3367 pyobject related functions pyobject related functions sing_195.htm#SEC235 3362 pyramid sing_23 86.htm#SEC246274213368 pyramid sing_2392.htm#SEC2468 7421 3363 3369 python_eval sing_196.htm#SEC236 3364 3370 python_import sing_197.htm#SEC237 3365 3371 python_run sing_198.htm#SEC238 3366 qbase sing_199 1.htm#SEC206786333367 qepcad sing_2 396.htm#SEC2472391713368 qepcadsystem sing_2 397.htm#SEC2473319773369 qhmatrix sing_162 5.htm#SEC1701618133370 qhmoduli.lib sing_15 89.htm#SEC16653371 qhmoduli_lib sing_15 89.htm#SEC16653372 qhspectrum sing_161 2.htm#SEC1688137323372 qbase sing_1993.htm#SEC2069 8633 3373 qepcad sing_2402.htm#SEC2478 39171 3374 qepcadsystem sing_2403.htm#SEC2479 31977 3375 qhmatrix sing_1627.htm#SEC1703 61813 3376 qhmoduli.lib sing_1591.htm#SEC1667 3377 qhmoduli_lib sing_1591.htm#SEC1667 3378 qhspectrum sing_1614.htm#SEC1690 13732 3373 3379 qhweight sing_327.htm#SEC367 3374 3380 qmatrix.lib sing_752.htm#SEC804 … … 3382 3388 qring declaration (plural) qring declaration (plural) sing_444.htm#SEC484 3383 3389 qring related functions (plural) qring related functions (plural) sing_445.htm#SEC485 3384 qring ring ideal 'factor ring' sing_102 4.htm#IDX5093390 qring ring ideal 'factor ring' sing_1026.htm#IDX502 3385 3391 qringNF, option sing_315.htm#IDX164 3386 3392 qslimgb sing_895.htm#SEC971 51999 3387 quadraticSieve sing_190 3.htm#SEC1979585573393 quadraticSieve sing_1905.htm#SEC1981 58557 3388 3394 quantMat sing_753.htm#SEC805 56227 3389 quickclass sing_149 5.htm#SEC1571140183395 quickclass sing_1497.htm#SEC1573 14018 3390 3396 quit sing_390.htm#SEC430 3391 quotSheaf sing_27 14.htm#SEC2790496193397 quotSheaf sing_2721.htm#SEC2797 49619 3392 3398 quote sing_329.htm#SEC369 3393 3399 quotient sing_330.htm#SEC370 3394 3400 quotient (plural) sing_476.htm#SEC516 3395 quotientLatticeBasis quotientLatticeBasis sing_204 4.htm#SEC2120156133396 quotientMain sing_175 3.htm#SEC1829398703397 quotientMon sing_1 198.htm#SEC1274571493398 rHRR sing_230 2.htm#SEC2378201313399 rJanet sing_26 89.htm#SEC2765307163400 rMacaulay sing_9 48.htm#SEC1024454993401 rad_con sing_97 5.htm#SEC1051217773402 radical sing_1 299.htm#SEC137514073403 radicalEHV sing_130 0.htm#SEC1376337033404 radicalMemberShip sing_215 2.htm#SEC2228285273405 radicalMon sing_1 199.htm#SEC1275649123406 radicalZ sing_131 4.htm#SEC139057833407 randcharpoly sing_198 5.htm#SEC2061377373408 randlinpoly sing_198 7.htm#SEC2063223303401 quotientLatticeBasis quotientLatticeBasis sing_2046.htm#SEC2122 15613 3402 quotientMain sing_1755.htm#SEC1831 39870 3403 quotientMon sing_1200.htm#SEC1276 57149 3404 rHRR sing_2304.htm#SEC2380 20131 3405 rJanet sing_2696.htm#SEC2772 30716 3406 rMacaulay sing_950.htm#SEC1026 45499 3407 rad_con sing_977.htm#SEC1053 21777 3408 radical sing_1301.htm#SEC1377 1407 3409 radicalEHV sing_1302.htm#SEC1378 33703 3410 radicalMemberShip sing_2154.htm#SEC2230 28527 3411 radicalMon sing_1201.htm#SEC1277 64912 3412 radicalZ sing_1316.htm#SEC1392 5783 3413 randcharpoly sing_1987.htm#SEC2063 37737 3414 randlinpoly sing_1989.htm#SEC2065 22330 3409 3415 random sing_331.htm#SEC371 3410 3416 random sing_358.htm#IDX244 3411 random sing_219 7.htm#IDX8763412 random sing_2 198.htm#IDX8783417 random sing_2199.htm#IDX869 3418 random sing_2200.htm#IDX871 3413 3419 random number generator, seed sing_358.htm#IDX242 3414 random.lib sing_98 3.htm#SEC10593415 randomBinomial sing_99 5.htm#SEC1071179133416 randomCheck sing_181 6.htm#SEC1892209733417 randomLast sing_99 4.htm#SEC107020463418 randomPoint sing_204 5.htm#SEC2121225613419 randomPolyInT sing_216 1.htm#SEC223722643420 random_lib sing_98 3.htm#SEC10593421 randomid sing_98 5.htm#SEC106178153422 randommat sing_98 6.htm#SEC1062335693420 random.lib sing_985.htm#SEC1061 3421 randomBinomial sing_997.htm#SEC1073 17913 3422 randomCheck sing_1818.htm#SEC1894 20973 3423 randomLast sing_996.htm#SEC1072 2046 3424 randomPoint sing_2047.htm#SEC2123 22561 3425 randomPolyInT sing_2163.htm#SEC2239 2264 3426 random_lib sing_985.htm#SEC1061 3427 randomid sing_987.htm#SEC1063 7815 3428 randommat sing_988.htm#SEC1064 33569 3423 3429 rank sing_209.htm#IDX137 3424 3430 rank sing_332.htm#SEC372 3425 rankSheaf sing_27 06.htm#SEC2782118503431 rankSheaf sing_2713.htm#SEC2789 11850 3426 3432 ratSol sing_788.htm#SEC840 62488 3427 3433 ratgb.lib sing_778.htm#IDX375 3428 3434 ratgb_lib sing_778.htm#IDX376 3429 rational curves, rational parametrization of rational curves. paraPlaneCurve sing_137 7.htm#IDX6233430 rational normal curve, projection. sing_13 78.htm#IDX6243431 rational normal curve, projection. sing_138 1.htm#IDX6253432 rational normal curve, projection. sing_138 2.htm#IDX6263435 rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1379.htm#IDX616 3436 rational normal curve, projection. sing_1380.htm#IDX617 3437 rational normal curve, projection. sing_1383.htm#IDX618 3438 rational normal curve, projection. sing_1384.htm#IDX619 3433 3439 rational solutions sing_780.htm#IDX387 3434 rational univariate projection sing_198 5.htm#IDX8103435 rationalCurve sing_27 26.htm#SEC2802612013436 rationalPointConic sing_13 79.htm#SEC145597613440 rational univariate projection sing_1987.htm#IDX803 3441 rationalCurve sing_2733.htm#SEC2809 61201 3442 rationalPointConic sing_1381.htm#SEC1457 9761 3437 3443 ratstd sing_779.htm#SEC831 61346 3438 rays sing_204 6.htm#SEC2122444453439 rcolon sing_2 596.htm#SEC267212083440 re2squ sing_135 6.htm#SEC1432243503444 rays sing_2048.htm#SEC2124 44445 3445 rcolon sing_2603.htm#SEC2679 1208 3446 re2squ sing_1358.htm#SEC1434 24350 3441 3447 read sing_333.htm#SEC373 3442 readNmzData sing_127 4.htm#SEC1350189573448 readNmzData sing_1276.htm#SEC1352 18957 3443 3449 reading, option sing_315.htm#IDX183 3444 3450 readline sing_1.htm#IDX5 3445 3451 real sing_28.htm#IDX74 3446 real root isolation sing_26 73.htm#IDX10303447 real roots, univariate polynomial sing_199 2.htm#IDX8123448 real roots, univariate projection sing_197 6.htm#IDX8083449 real roots,sign conditions sing_17 59.htm#IDX7883450 realclassify sing_26 68.htm#SEC2744514163451 realclassify.lib sing_26 67.htm#SEC27433452 realclassify_lib sing_26 67.htm#SEC27433453 realizationDim sing_212 4.htm#SEC2200377563454 realizationDimPoly sing_212 6.htm#SEC220236113455 realizationMatroids.lib realizationMatroids_lib sing_212 3.htm#SEC21993456 realizationMatroids_lib realizationMatroids_lib sing_212 3.htm#SEC21993457 realmorsesplit sing_26 69.htm#SEC2745163183458 realpoly sing_132 3.htm#SEC139994533459 realrad sing_132 5.htm#SEC1401433813460 realrad.lib sing_132 2.htm#SEC13983461 realrad_lib sing_132 2.htm#SEC13983462 realzero sing_132 4.htm#SEC1400127123463 recursive_boolean_poly recursive_boolean_poly sing_223 0.htm#SEC2306170453464 recursive_from_boolean_poly recursive_from_boolean_poly sing_223 6.htm#SEC2312377943452 real root isolation sing_2680.htm#IDX1028 3453 real roots, univariate polynomial sing_1994.htm#IDX805 3454 real roots, univariate projection sing_1978.htm#IDX801 3455 real roots,sign conditions sing_1761.htm#IDX781 3456 realclassify sing_2675.htm#SEC2751 51416 3457 realclassify.lib sing_2674.htm#SEC2750 3458 realclassify_lib sing_2674.htm#SEC2750 3459 realizationDim sing_2126.htm#SEC2202 37756 3460 realizationDimPoly sing_2128.htm#SEC2204 3611 3461 realizationMatroids.lib realizationMatroids_lib sing_2125.htm#SEC2201 3462 realizationMatroids_lib realizationMatroids_lib sing_2125.htm#SEC2201 3463 realmorsesplit sing_2676.htm#SEC2752 16318 3464 realpoly sing_1325.htm#SEC1401 9453 3465 realrad sing_1327.htm#SEC1403 43381 3466 realrad.lib sing_1324.htm#SEC1400 3467 realrad_lib sing_1324.htm#SEC1400 3468 realzero sing_1326.htm#SEC1402 12712 3469 recursive_boolean_poly recursive_boolean_poly sing_2232.htm#SEC2308 17045 3470 recursive_from_boolean_poly recursive_from_boolean_poly sing_2238.htm#SEC2314 37794 3465 3471 redSB, option sing_315.htm#IDX165 3466 3472 redTail, option sing_315.htm#IDX167 … … 3469 3475 reduce sing_334.htm#SEC374 3470 3476 reduce sing_519.htm#IDX324 3471 reduce sing_926.htm#IDX4 403472 reduce sing_927.htm#IDX4 433477 reduce sing_926.htm#IDX431 3478 reduce sing_927.htm#IDX434 3473 3479 reduce (plural) sing_477.htm#SEC517 3474 3480 reduce (up to a bound) sing_358.htm#IDX245 3475 reduceIntChain sing_253 2.htm#SEC2608177763476 reduced sing_925.htm#IDX4 373481 reduceIntChain sing_2539.htm#SEC2615 17776 3482 reduced sing_925.htm#IDX428 3477 3483 reduced standard basis sing_315.htm#IDX166 3478 reduction sing_167 7.htm#SEC1753310483479 reesclos.lib sing_132 6.htm#SEC14023480 reesclos_lib sing_132 6.htm#SEC14023484 reduction sing_1679.htm#SEC1755 31048 3485 reesclos.lib sing_1328.htm#SEC1404 3486 reesclos_lib sing_1328.htm#SEC1404 3481 3487 reference sing_199.htm#SEC239 3482 3488 reference declarations reference declarations sing_200.htm#SEC240 … … 3484 3490 reference operations reference and shared operations sing_204.htm#SEC244 3485 3491 reference related functions reference and shared related functions sing_205.htm#SEC245 3486 regCM sing_12 38.htm#SEC1314254883487 regIdeal sing_122 4.htm#SEC130038273488 regMonCurve sing_122 7.htm#SEC1303413113492 regCM sing_1240.htm#SEC1316 25488 3493 regIdeal sing_1226.htm#SEC1302 3827 3494 regMonCurve sing_1229.htm#SEC1305 41311 3489 3495 regularity Syzygies and resolutions sing_335.htm#SEC375 3490 3496 regularity sing_870.htm#SEC927 3491 3497 reiffen sing_558.htm#SEC610 32856 3492 rel_orbit_variety sing_167 0.htm#SEC1746342783498 rel_orbit_variety sing_1672.htm#SEC1748 34278 3493 3499 relations sing_750.htm#IDX364 3494 relativeInteriorPoint relativeInteriorPoint sing_204 7.htm#SEC2123300973495 relative_orbit_variety relative_orbit_variety sing_167 1.htm#SEC1747329953496 relweight sing_162 6.htm#SEC1702106583497 remainder sing_174 6.htm#SEC182211913498 remainderMain sing_175 4.htm#SEC183035323499 removeCone sing_206 5.htm#SEC2141338773500 removepower sing_148 3.htm#SEC1559476443500 relativeInteriorPoint relativeInteriorPoint sing_2049.htm#SEC2125 30097 3501 relative_orbit_variety relative_orbit_variety sing_1673.htm#SEC1749 32995 3502 relweight sing_1628.htm#SEC1704 10658 3503 remainder sing_1748.htm#SEC1824 1191 3504 remainderMain sing_1756.htm#SEC1832 3532 3505 removeCone sing_2067.htm#SEC2143 33877 3506 removepower sing_1485.htm#SEC1561 47644 3501 3507 repart sing_336.htm#SEC376 3502 replace sing_185 5.htm#SEC1931500753508 replace sing_1857.htm#SEC1933 50075 3503 3509 representation, math objects Representation of mathematical objects sing_856.htm#SEC908 3504 3510 res sing_337.htm#SEC377 10393 3505 resbinomial.lib sing_138 6.htm#IDX6293506 resbinomial_lib sing_138 6.htm#IDX6303511 resbinomial.lib sing_1388.htm#IDX622 3512 resbinomial_lib sing_1388.htm#IDX623 3507 3513 reservedName sing_338.htm#SEC378 3508 resfunction sing_140 0.htm#SEC1476593123509 resgraph.lib sing_14 18.htm#SEC14943510 resgraph_lib sing_14 18.htm#SEC14943511 resjung.lib sing_142 2.htm#SEC14983512 resjung_lib sing_142 2.htm#SEC14983513 reslist sing_141 4.htm#SEC1490649503514 resfunction sing_1402.htm#SEC1478 59312 3515 resgraph.lib sing_1420.htm#SEC1496 3516 resgraph_lib sing_1420.htm#SEC1496 3517 resjung.lib sing_1424.htm#SEC1500 3518 resjung_lib sing_1424.htm#SEC1500 3519 reslist sing_1416.htm#SEC1492 64950 3514 3520 resolution purityfiltration_lib sing_161.htm#SEC201 3515 3521 resolution sing_758.htm#IDX371 … … 3519 3525 resolution expressions resolution expressions sing_163.htm#SEC203 3520 3526 resolution expressions (plural) resolution expressions (plural) sing_448.htm#SEC488 3521 resolution graph sing_14 68.htm#IDX6433527 resolution graph sing_1470.htm#IDX636 3522 3528 resolution related functions resolution related functions sing_164.htm#SEC204 3523 3529 resolution related functions (plural) resolution related functions (plural) sing_449.htm#SEC489 … … 3525 3531 resolution, computation of sing_337.htm#IDX186 3526 3532 resolution, hilbert-driven sing_263.htm#SEC303 3527 resolutionInLocalization resolutionInLocalization sing_241 3.htm#SEC2489311063528 resolutiongraph sing_14 69.htm#SEC1545326973529 resolve sing_143 0.htm#SEC1506273743530 resolve.lib sing_142 6.htm#SEC15023531 resolve_lib sing_142 6.htm#SEC15023532 resources.lib sing_99 6.htm#SEC10723533 resources_lib sing_99 6.htm#SEC10723534 restriction sing_219 0.htm#IDX8643535 restriction sing_220 6.htm#IDX8973536 restriction sing_220 7.htm#IDX8993533 resolutionInLocalization resolutionInLocalization sing_2419.htm#SEC2495 31106 3534 resolutiongraph sing_1471.htm#SEC1547 32697 3535 resolve sing_1432.htm#SEC1508 27374 3536 resolve.lib sing_1428.htm#SEC1504 3537 resolve_lib sing_1428.htm#SEC1504 3538 resources.lib sing_998.htm#SEC1074 3539 resources_lib sing_998.htm#SEC1074 3540 restriction sing_2192.htm#IDX857 3541 restriction sing_2208.htm#IDX890 3542 restriction sing_2209.htm#IDX892 3537 3543 restriction of sing_563.htm#IDX347 3538 3544 restrictionIdeal sing_573.htm#SEC625 49796 … … 3540 3546 resultant sing_302.htm#SEC342 3541 3547 resultant sing_339.htm#SEC379 3542 reszeta.lib sing_14 39.htm#SEC15153543 reszeta_lib sing_14 39.htm#SEC15153548 reszeta.lib sing_1441.htm#SEC1517 3549 reszeta_lib sing_1441.htm#SEC1517 3544 3550 return sing_391.htm#SEC431 3545 3551 return type of procedures Return type of procedures sing_416.htm#SEC456 3546 3552 returnSB, option sing_315.htm#IDX152 3547 reverse sing_200 6.htm#SEC2082358803553 reverse sing_2008.htm#SEC2084 35880 3548 3554 reverse lexicographical ordering sing_860.htm#IDX392 3549 reynolds_molien sing_164 6.htm#SEC1722453163550 rho sing_189 7.htm#SEC1973514143551 rightInverse sing_183 5.htm#SEC191165583552 rightKernel sing_183 3.htm#SEC1909466033555 reynolds_molien sing_1648.htm#SEC1724 45316 3556 rho sing_1899.htm#SEC1975 51414 3557 rightInverse sing_1837.htm#SEC1913 6558 3558 rightKernel sing_1835.htm#SEC1911 46603 3553 3559 rightModulo sing_737.htm#SEC789 12618 3554 3560 rightNF sing_736.htm#SEC788 42610 3555 3561 rightNFWeyl sing_805.htm#SEC857 35828 3556 rightOre sing_26 53.htm#SEC2729569183562 rightOre sing_2660.htm#SEC2736 56918 3557 3563 rightStd sing_735.htm#SEC787 5740 3558 3564 ring sing_165.htm#SEC205 3559 3565 ring (plural) sing_450.htm#SEC490 3560 ring coefficients hasTransExtensionCoefficient sing_102 2.htm#IDX5073561 ring coefficients sing_102 3.htm#IDX5083566 ring coefficients hasTransExtensionCoefficient sing_1024.htm#IDX500 3567 ring coefficients sing_1025.htm#IDX501 3562 3568 ring declarations sing_167.htm#SEC207 3563 3569 ring declarations (plural) ring declarations (plural) sing_451.htm#SEC491 … … 3567 3573 ring related functions (plural) ring related functions (plural) sing_453.htm#SEC493 3568 3574 ring, opposite sing_358.htm#IDX229 3569 ring.lib sing_100 1.htm#SEC10773575 ring.lib sing_1003.htm#SEC1079 3570 3576 ring_cf sing_209.htm#IDX138 3571 ring_lib sing_100 1.htm#SEC10773577 ring_lib sing_1003.htm#SEC1079 3572 3578 ring_list sing_341.htm#SEC381 3573 ring_variable sing_217 7.htm#IDX8413574 ring_variable sing_21 78.htm#IDX8433575 ring_variable sing_21 79.htm#IDX8473576 ring_variable sing_218 0.htm#IDX8493579 ring_variable sing_2179.htm#IDX834 3580 ring_variable sing_2180.htm#IDX836 3581 ring_variable sing_2181.htm#IDX840 3582 ring_variable sing_2182.htm#IDX842 3577 3583 ringlist sing_340.htm#SEC380 3578 3584 ringlist (plural) sing_478.htm#SEC518 3579 ringtensor sing_101 3.htm#SEC1089566483580 ringweights sing_101 4.htm#SEC1090333073581 rinvar.lib sing_168 2.htm#SEC17583582 rinvar_lib sing_168 2.htm#SEC17583583 rmNmzFiles sing_12 79.htm#SEC1355326013584 rm_unitcol sing_107 2.htm#SEC114855913585 rm_unitrow sing_107 1.htm#SEC1147356943586 rmx sing_178 0.htm#SEC1856176753587 rncAntiCanonicalMap sing_13 78.htm#SEC1454419653588 rncItProjEven sing_138 2.htm#SEC1458182003589 rncItProjOdd sing_138 1.htm#SEC1457619763585 ringtensor sing_1015.htm#SEC1091 56648 3586 ringweights sing_1016.htm#SEC1092 33307 3587 rinvar.lib sing_1684.htm#SEC1760 3588 rinvar_lib sing_1684.htm#SEC1760 3589 rmNmzFiles sing_1281.htm#SEC1357 32601 3590 rm_unitcol sing_1074.htm#SEC1150 5591 3591 rm_unitrow sing_1073.htm#SEC1149 35694 3592 rmx sing_1782.htm#SEC1858 17675 3593 rncAntiCanonicalMap sing_1380.htm#SEC1456 41965 3594 rncItProjEven sing_1384.htm#SEC1460 18200 3595 rncItProjOdd sing_1383.htm#SEC1459 61976 3590 3596 root of Bernstein-Sato polynomial sing_540.htm#IDX336 3591 rootIsolation sing_26 84.htm#SEC2760345133592 rootIsolationNoPreprocessing rootIsolationNoPreprocessing sing_26 83.htm#SEC2759423873593 rootIsolationPrimdec rootIsolationPrimdec sing_26 85.htm#SEC2761354853594 rootisolation.lib sing_26 73.htm#SEC27493595 rootisolation_lib sing_26 73.htm#SEC27493596 rootofUnity sing_101 6.htm#SEC1092213653597 roots sing_174 7.htm#SEC1823184363598 rootsMain sing_175 5.htm#SEC1831549343599 rootsModp sing_18 79.htm#SEC1955473153600 rootsmr.lib sing_197 6.htm#SEC20523601 rootsmr_lib sing_197 6.htm#SEC20523602 rootsur.lib sing_199 2.htm#SEC20683603 rootsur_lib sing_199 2.htm#SEC20683604 round sing_187 7.htm#SEC195392483597 rootIsolation sing_2691.htm#SEC2767 34513 3598 rootIsolationNoPreprocessing rootIsolationNoPreprocessing sing_2690.htm#SEC2766 42387 3599 rootIsolationPrimdec rootIsolationPrimdec sing_2692.htm#SEC2768 35485 3600 rootisolation.lib sing_2680.htm#SEC2756 3601 rootisolation_lib sing_2680.htm#SEC2756 3602 rootofUnity sing_1018.htm#SEC1094 21365 3603 roots sing_1749.htm#SEC1825 18436 3604 rootsMain sing_1757.htm#SEC1833 54934 3605 rootsModp sing_1881.htm#SEC1957 47315 3606 rootsmr.lib sing_1978.htm#SEC2054 3607 rootsmr_lib sing_1978.htm#SEC2054 3608 rootsur.lib sing_1994.htm#SEC2070 3609 rootsur_lib sing_1994.htm#SEC2070 3610 round sing_1879.htm#SEC1955 9248 3605 3611 rowShift sing_209.htm#IDX141 3606 3612 rowShift sing_211.htm#SEC251 3607 rowred sing_10 68.htm#SEC1144634163613 rowred sing_1070.htm#SEC1146 63416 3608 3614 rp, global ordering sing_860.htm#IDX391 3609 rstandard.lib sing_26 86.htm#SEC27623610 rstandard_lib sing_26 86.htm#SEC27623611 rswalk sing_27 36.htm#SEC2812509033615 rstandard.lib sing_2693.htm#SEC2769 3616 rstandard_lib sing_2693.htm#SEC2769 3617 rswalk sing_2743.htm#SEC2819 50903 3612 3618 rtimer sing_404.htm#SEC444 3613 3619 rvalue No rvalue of increments and assignments sing_410.htm#SEC450 3614 3620 rvar sing_342.htm#SEC382 3615 rwalk sing_2 693.htm#SEC2769425253616 rwalk.lib sing_269 1.htm#SEC27673617 rwalk_lib sing_269 1.htm#SEC27673618 sRes sing_2 498.htm#SEC2574233813621 rwalk sing_2700.htm#SEC2776 42525 3622 rwalk.lib sing_2698.htm#SEC2774 3623 rwalk_lib sing_2698.htm#SEC2774 3624 sRes sing_2505.htm#SEC2581 23381 3619 3625 sa_poly_reduce sing_528.htm#SEC580 60856 3620 3626 sa_reduce sing_527.htm#SEC579 55799 3621 sagbi sing_133 2.htm#SEC1408466533622 sagbi basis sing_233 0.htm#IDX9493623 sagbi.lib sing_13 29.htm#SEC14053624 sagbiAlg sing_232 3.htm#SEC2399sprintf3625 sagbiMod sing_232 4.htm#SEC2400sprintf3626 sagbiPart sing_133 3.htm#SEC1409560663627 sagbiReduce sing_133 1.htm#SEC1407190363628 sagbiSPoly sing_133 0.htm#SEC1406173653629 sagbi_lib sing_13 29.htm#SEC14053630 salida sing_141 1.htm#SEC148798393631 sameComponent sing_19 59.htm#SEC2035135403632 sameQ sing_17 58.htm#SEC1834455793633 sat sing_113 7.htm#SEC121362663634 satiety sing_122 6.htm#SEC1302343233635 satstd sing_22 18.htm#SEC2294161283627 sagbi sing_1334.htm#SEC1410 46653 3628 sagbi basis sing_2332.htm#IDX942 3629 sagbi.lib sing_1331.htm#SEC1407 3630 sagbiAlg sing_2325.htm#SEC2401 sprintf 3631 sagbiMod sing_2326.htm#SEC2402 sprintf 3632 sagbiPart sing_1335.htm#SEC1411 56066 3633 sagbiReduce sing_1333.htm#SEC1409 19036 3634 sagbiSPoly sing_1332.htm#SEC1408 17365 3635 sagbi_lib sing_1331.htm#SEC1407 3636 salida sing_1413.htm#SEC1489 9839 3637 sameComponent sing_1961.htm#SEC2037 13540 3638 sameQ sing_1760.htm#SEC1836 45579 3639 sat sing_1139.htm#SEC1215 6266 3640 satiety sing_1228.htm#SEC1304 34323 3641 satstd sing_2220.htm#SEC2296 16128 3636 3642 sba sing_343.htm#SEC383 3637 3643 scalarProd sing_517.htm#SEC569 54488 3638 scheme sing_23 77.htm#SEC2453157223639 schubert.lib sing_2 695.htm#SEC27713640 schubert_lib sing_2 695.htm#SEC27713644 scheme sing_2383.htm#SEC2459 15722 3645 schubert.lib sing_2702.htm#SEC2778 3646 schubert_lib sing_2702.htm#SEC2778 3641 3647 sdb, source code debugger Source code debugger sing_66.htm#SEC103 3642 second degree sing_942.htm#IDX4 893643 secondary fan sing_20 69.htm#IDX8153644 secondary polytope sing_20 69.htm#IDX8163645 secondaryPolytope sing_207 4.htm#SEC2150484513646 secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_166 7.htm#SEC1743370583647 secondary_char0 sing_166 2.htm#SEC1738310293648 secondary_charp sing_166 4.htm#SEC1740163643649 secondary_no_molien sing_166 5.htm#SEC174136163650 secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_16 68.htm#SEC1744316753651 segre sing_225 7.htm#SEC2333440353652 select sing_11 38.htm#SEC1214170963653 select1 sing_11 39.htm#SEC1215326173648 second degree sing_942.htm#IDX479 3649 secondary fan sing_2071.htm#IDX808 3650 secondary polytope sing_2071.htm#IDX809 3651 secondaryPolytope sing_2076.htm#SEC2152 48451 3652 secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1669.htm#SEC1745 37058 3653 secondary_char0 sing_1664.htm#SEC1740 31029 3654 secondary_charp sing_1666.htm#SEC1742 16364 3655 secondary_no_molien sing_1667.htm#SEC1743 3616 3656 secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1670.htm#SEC1746 31675 3657 segre sing_2259.htm#SEC2335 44035 3658 select sing_1140.htm#SEC1216 17096 3659 select1 sing_1141.htm#SEC1217 32617 3654 3660 semaphore sing_358.htm#IDX249 44342 3655 semaphore sing_100 0.htm#SEC10763656 semaphores sing_99 6.htm#IDX5023657 semiCMcod2 sing_162 3.htm#SEC1699159053658 semiGroup sing_232 5.htm#SEC2401sprintf3659 semiMod sing_232 6.htm#SEC2402sprintf3660 semidiv sing_195 1.htm#SEC2027581073661 semigroup sing_147 2.htm#SEC1548290453662 semigroup sing_147 6.htm#IDX6503663 semigroup of values sing_156 2.htm#IDX7653664 semigroupGenerator sing_20 48.htm#SEC2124594463665 sep sing_13 09.htm#SEC1385sprintf3666 separateHNE sing_157 3.htm#SEC1649120523667 separator sing_12 09.htm#SEC1285330003661 semaphore sing_1002.htm#SEC1078 3662 semaphores sing_998.htm#IDX495 3663 semiCMcod2 sing_1625.htm#SEC1701 15905 3664 semiGroup sing_2327.htm#SEC2403 sprintf 3665 semiMod sing_2328.htm#SEC2404 sprintf 3666 semidiv sing_1953.htm#SEC2029 58107 3667 semigroup sing_1474.htm#SEC1550 29045 3668 semigroup sing_1478.htm#IDX643 3669 semigroup of values sing_1564.htm#IDX758 3670 semigroupGenerator sing_2050.htm#SEC2126 59446 3671 sep sing_1311.htm#SEC1387 sprintf 3672 separateHNE sing_1575.htm#SEC1651 12052 3673 separator sing_1211.htm#SEC1287 33000 3668 3674 serreRelations sing_658.htm#SEC710 33994 3669 set sing_217 2.htm#IDX8273670 setBaseMultigrading sing_25 43.htm#SEC261965753675 set sing_2174.htm#IDX820 3676 setBaseMultigrading sing_2550.htm#SEC2626 6575 3671 3677 setLetterplaceAttributes setLetterplaceAttributes sing_648.htm#SEC700 5759 3672 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49.htm#SEC1025155993700 showBO sing_143 1.htm#SEC1507200893701 showDataTypes sing_143 3.htm#SEC150942703702 showNmzOptions sing_127 0.htm#SEC1346649553703 showNuminvs sing_126 7.htm#SEC1343189343705 show sing_951.htm#SEC1027 15599 3706 showBO sing_1433.htm#SEC1509 20089 3707 showDataTypes sing_1435.htm#SEC1511 4270 3708 showNmzOptions sing_1272.htm#SEC1348 64955 3709 showNuminvs sing_1269.htm#SEC1345 18934 3704 3710 showgrades sing_763.htm#SEC815 48081 3705 showrecursive sing_95 0.htm#SEC102661273711 showrecursive sing_952.htm#SEC1028 6127 3706 3712 sickle sing_624.htm#SEC676 54811 3707 signal handler sing_27 54.htm#SEC28433708 signatureBrieskorn sing_163 2.htm#SEC1708262833709 signatureL sing_222 0.htm#SEC2296654933710 signatureLqf sing_222 1.htm#SEC2297188113711 signatureNemethi sing_163 4.htm#SEC1710219813712 signaturePuiseux sing_163 3.htm#SEC1709233983713 signcnd sing_176 0.htm#SEC1836401473714 signcond.lib sing_17 59.htm#SEC18353715 signcond_lib sing_17 59.htm#SEC18353716 simplePrune sing_25 36.htm#SEC2612sprintf3717 simplesolver sing_170 4.htm#SEC1780134183713 signal handler sing_2761.htm#SEC2850 3714 signatureBrieskorn sing_1634.htm#SEC1710 26283 3715 signatureL sing_2222.htm#SEC2298 65493 3716 signatureLqf sing_2223.htm#SEC2299 18811 3717 signatureNemethi sing_1636.htm#SEC1712 21981 3718 signaturePuiseux sing_1635.htm#SEC1711 23398 3719 signcnd sing_1762.htm#SEC1838 40147 3720 signcond.lib sing_1761.htm#SEC1837 3721 signcond_lib sing_1761.htm#SEC1837 3722 simplePrune sing_2543.htm#SEC2619 sprintf 3723 simplesolver sing_1706.htm#SEC1782 13418 3718 3724 simplex sing_345.htm#SEC385 3719 simplexOut sing_173 1.htm#SEC1807560993725 simplexOut sing_1733.htm#SEC1809 56099 3720 3726 simplify sing_346.htm#SEC386 3721 3727 simplifyRat sing_800.htm#SEC852 52658 3722 sing.lib sing_1 599.htm#SEC16753723 sing4ti2.lib sing_133 5.htm#SEC14113724 sing4ti2_lib sing_133 5.htm#SEC14113725 sing_lib sing_1 599.htm#SEC16753728 sing.lib sing_1601.htm#SEC1677 3729 sing4ti2.lib sing_1337.htm#SEC1413 3730 sing4ti2_lib sing_1337.htm#SEC1413 3731 sing_lib sing_1601.htm#SEC1677 3726 3732 singular locus of D-module sing_780.htm#IDX381 3727 singularities sing_153 1.htm#IDX6673728 singularities sing_153 2.htm#IDX6783729 singularities sing_153 3.htm#IDX6813730 singularities sing_153 4.htm#IDX6843731 singularities sing_153 5.htm#IDX6873732 singularities sing_153 6.htm#IDX6913733 singularities sing_153 7.htm#IDX6953734 singularities sing_15 38.htm#IDX7013735 singularities sing_15 39.htm#IDX7093736 singularities sing_154 0.htm#IDX7153737 singularities sing_154 1.htm#IDX7233738 singularities sing_154 2.htm#IDX7333739 singularities sing_163 0.htm#IDX7803740 singularities sing_23 19.htm#IDX9443733 singularities sing_1533.htm#IDX660 3734 singularities sing_1534.htm#IDX671 3735 singularities sing_1535.htm#IDX674 3736 singularities sing_1536.htm#IDX677 3737 singularities sing_1537.htm#IDX680 3738 singularities sing_1538.htm#IDX684 3739 singularities sing_1539.htm#IDX688 3740 singularities sing_1540.htm#IDX694 3741 singularities sing_1541.htm#IDX702 3742 singularities sing_1542.htm#IDX708 3743 singularities sing_1543.htm#IDX716 3744 singularities sing_1544.htm#IDX726 3745 singularities sing_1632.htm#IDX773 3746 singularities sing_2321.htm#IDX937 3741 3747 singularities, resolution of Resolution of singularities sing_843.htm#SEC895 3742 singularity sing_149 6.htm#SEC1572230023748 singularity sing_1498.htm#SEC1574 23002 3743 3749 singularrc sing_20.htm#IDX73 3744 3750 size Miscellaneous oddities sing_347.htm#SEC387 3745 3751 size sing_418.htm#IDX294 3746 skewmat sing_105 5.htm#SEC113121673752 skewmat sing_1057.htm#SEC1133 2167 3747 3753 sleep sing_353.htm#SEC393 3748 3754 slimgb sing_348.htm#SEC388 3749 3755 slimgb sing_820.htm#SEC872 3750 3756 slimgb (plural) sing_479.htm#SEC519 3751 slocus sing_161 1.htm#SEC1687278533752 smith sing_184 4.htm#SEC1920619153753 smithNormalForm sing_259 1.htm#SEC266771743754 solutionsMod2 sing_189 4.htm#SEC1970533603755 solve sing_942.htm#IDX4 90 30783756 solve sing_172 5.htm#SEC18013757 slocus sing_1613.htm#SEC1689 27853 3758 smith sing_1846.htm#SEC1922 61915 3759 smithNormalForm sing_2598.htm#SEC2674 7174 3760 solutionsMod2 sing_1896.htm#SEC1972 53360 3761 solve sing_942.htm#IDX480 3078 3762 solve sing_1727.htm#SEC1803 3757 3763 solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_291.htm#SEC331 3758 solve.lib sing_172 3.htm#SEC17993759 solveTInitialFormPar solveTInitialFormPar sing_215 5.htm#SEC2231366703760 solve_IP sing_118 2.htm#SEC1258595183761 solve_lib sing_172 3.htm#SEC17993762 solvelinearpart sing_17 18.htm#SEC1794428723764 solve.lib sing_1725.htm#SEC1801 3765 solveTInitialFormPar solveTInitialFormPar sing_2157.htm#SEC2233 36670 3766 solve_IP sing_1184.htm#SEC1260 59518 3767 solve_lib sing_1725.htm#SEC1801 3768 solvelinearpart sing_1720.htm#SEC1796 42872 3763 3769 sort sing_916.htm#SEC992 58207 3764 3770 sortIntvec sing_595.htm#SEC647 60798 3765 sortandmap sing_17 19.htm#SEC1795103143766 sortier sing_168 1.htm#SEC175735553767 sortvars sing_172 0.htm#SEC1796617783771 sortandmap sing_1721.htm#SEC1797 10314 3772 sortier sing_1683.htm#SEC1759 3555 3773 sortvars sing_1722.htm#SEC1798 61778 3768 3774 sortvec sing_349.htm#SEC389 3769 source sing_25 14.htm#SEC2590631633775 source sing_2521.htm#SEC2597 63163 3770 3776 source code debugger, sdb Source code debugger sing_66.htm#SEC103 3771 spaceCur sing_23 28.htm#SEC2404sprintf3772 spadd sing_154 5.htm#SEC1621487393773 span sing_205 1.htm#SEC2127643433774 sparseHomogIdeal sing_99 2.htm#SEC1068226313775 sparseInterpolation sing_237 2.htm#SEC2448287713776 sparseid sing_98 7.htm#SEC1063208243777 sparsemat sing_9 89.htm#SEC1065176533778 sparsematrix sing_9 88.htm#SEC1064410313779 sparsepoly sing_99 0.htm#SEC1066216493780 sparsetriag sing_99 1.htm#SEC1067506573781 spcurve.lib sing_16 19.htm#SEC16953782 spcurve_lib sing_16 19.htm#SEC16953777 spaceCur sing_2330.htm#SEC2406 sprintf 3778 spadd sing_1547.htm#SEC1623 48739 3779 span sing_2053.htm#SEC2129 64343 3780 sparseHomogIdeal sing_994.htm#SEC1070 22631 3781 sparseInterpolation sing_2378.htm#SEC2454 28771 3782 sparseid sing_989.htm#SEC1065 20824 3783 sparsemat sing_991.htm#SEC1067 17653 3784 sparsematrix sing_990.htm#SEC1066 41031 3785 sparsepoly sing_992.htm#SEC1068 21649 3786 sparsetriag sing_993.htm#SEC1069 50657 3787 spcurve.lib sing_1621.htm#SEC1697 3788 spcurve_lib sing_1621.htm#SEC1697 3783 3789 special characters, non-english sing_407.htm#IDX287 3784 spectral pairs sing_153 1.htm#IDX6763785 spectral pairs sing_15 38.htm#IDX7083786 spectral pairs sing_154 0.htm#IDX7223787 spectral pairs sing_154 1.htm#IDX7313788 spectral pairs sing_155 3.htm#IDX7473789 spectral pairs sing_155 5.htm#IDX7583790 spectralNeg sing_144 1.htm#SEC1517366913791 spectrum sing_153 1.htm#IDX675475453792 spectrum sing_153 7.htm#SEC16133793 spectrum sing_153 7.htm#IDX7003794 spectrum sing_15 38.htm#IDX7073795 spectrum sing_15 39.htm#IDX7143796 spectrum sing_154 0.htm#IDX7213797 spectrum sing_154 1.htm#IDX7303798 spectrum sing_155 3.htm#IDX7463799 spectrum sing_155 5.htm#IDX7573800 spectrum sing_163 0.htm#IDX7823801 spectrum.lib sing_16 29.htm#SEC17053802 spectrum_lib sing_16 29.htm#SEC17053803 spectrumnd sing_163 0.htm#SEC1706299433804 spgamma sing_155 2.htm#SEC1628596533805 spgeomgenus sing_155 1.htm#SEC1627577963806 spissemicont sing_15 48.htm#SEC1624236793807 split sing_95 1.htm#SEC1027297943808 splitPolygon sing_207 6.htm#SEC21527063809 splitring sing_132 1.htm#SEC1397564043810 splitting sing_121 7.htm#SEC1293347343811 spmilnor sing_155 0.htm#SEC1626329333812 spmul sing_154 7.htm#SEC1623436073813 spnf sing_1 098.htm#SEC1174573093814 spoly sing_196 2.htm#SEC2038354543815 sppairs sing_15 38.htm#SEC1614495133816 sppnf sing_154 3.htm#SEC1619166503817 sppprint sing_154 4.htm#SEC1620436823818 spprint sing_1 099.htm#SEC1175186713790 spectral pairs sing_1533.htm#IDX669 3791 spectral pairs sing_1540.htm#IDX701 3792 spectral pairs sing_1542.htm#IDX715 3793 spectral pairs sing_1543.htm#IDX724 3794 spectral pairs sing_1555.htm#IDX740 3795 spectral pairs sing_1557.htm#IDX751 3796 spectralNeg sing_1443.htm#SEC1519 36691 3797 spectrum sing_1533.htm#IDX668 47545 3798 spectrum sing_1539.htm#SEC1615 3799 spectrum sing_1539.htm#IDX693 3800 spectrum sing_1540.htm#IDX700 3801 spectrum sing_1541.htm#IDX707 3802 spectrum sing_1542.htm#IDX714 3803 spectrum sing_1543.htm#IDX723 3804 spectrum sing_1555.htm#IDX739 3805 spectrum sing_1557.htm#IDX750 3806 spectrum sing_1632.htm#IDX775 3807 spectrum.lib sing_1631.htm#SEC1707 3808 spectrum_lib sing_1631.htm#SEC1707 3809 spectrumnd sing_1632.htm#SEC1708 29943 3810 spgamma sing_1554.htm#SEC1630 59653 3811 spgeomgenus sing_1553.htm#SEC1629 57796 3812 spissemicont sing_1550.htm#SEC1626 23679 3813 split sing_953.htm#SEC1029 29794 3814 splitPolygon sing_2078.htm#SEC2154 706 3815 splitring sing_1323.htm#SEC1399 56404 3816 splitting sing_1219.htm#SEC1295 34734 3817 spmilnor sing_1552.htm#SEC1628 32933 3818 spmul sing_1549.htm#SEC1625 43607 3819 spnf sing_1100.htm#SEC1176 57309 3820 spoly sing_1964.htm#SEC2040 35454 3821 sppairs sing_1540.htm#SEC1616 49513 3822 sppnf sing_1545.htm#SEC1621 16650 3823 sppprint sing_1546.htm#SEC1622 43682 3824 spprint sing_1101.htm#SEC1177 18671 3819 3825 sprintf sing_351.htm#SEC391 55889 3820 spsemicont sing_15 49.htm#SEC1625611693821 spsub sing_154 6.htm#SEC1622542963822 sqfrNorm sing_17 48.htm#SEC1824205463823 sqfrNormMain sing_175 6.htm#SEC183298903824 sqr sing_187 4.htm#SEC1950sprintf3826 spsemicont sing_1551.htm#SEC1627 61169 3827 spsub sing_1548.htm#SEC1624 54296 3828 sqfrNorm sing_1750.htm#SEC1826 20546 3829 sqfrNormMain sing_1758.htm#SEC1834 9890 3830 sqr sing_1876.htm#SEC1952 sprintf 3825 3831 sqrfree sing_350.htm#SEC390 3826 squareRoot sing_189 3.htm#SEC1969174463827 squarefree sing_157 4.htm#SEC1650484853832 squareRoot sing_1895.htm#SEC1971 17446 3833 squarefree sing_1576.htm#SEC1652 48485 3828 3834 sres sing_352.htm#SEC392 3829 3835 ssi Parallelization with ssi links sing_815.htm#SEC867 3830 stabilizer sing_22 48.htm#SEC2324366923831 stack, moduli space of stable maps sing_27 19.htm#IDX10593832 stack, moduli space of stable maps, rational curves moduliSpace sing_27 18.htm#IDX10583833 stackNets sing_264 0.htm#SEC2716309743834 staircase sing_176 5.htm#SEC1841497813835 standard sing_19 69.htm#SEC2045140673836 standard bases, saturation sing_22 18.htm#IDX9103837 standard bases. sing_221 7.htm#IDX9093836 stabilizer sing_2250.htm#SEC2326 36692 3837 stack, moduli space of stable maps sing_2726.htm#IDX1057 3838 stack, moduli space of stable maps, rational curves moduliSpace sing_2725.htm#IDX1056 3839 stackNets sing_2647.htm#SEC2723 30974 3840 staircase sing_1767.htm#SEC1843 49781 3841 standard sing_1971.htm#SEC2047 14067 3842 standard bases, saturation sing_2220.htm#IDX903 3843 standard bases. sing_2219.htm#IDX902 3838 3844 standard.lib sing_894.htm#IDX419 3839 3845 standard_lib sing_894.htm#IDX420 3840 startNmz sing_12 78.htm#SEC1354219253841 startTasks sing_103 5.htm#SEC1111167153846 startNmz sing_1280.htm#SEC1356 21925 3847 startTasks sing_1037.htm#SEC1113 16715 3842 3848 static procedures Procedure definition sing_43.htm#SEC78 3843 3849 status sing_353.htm#SEC393 … … 3848 3854 stdhilb sing_356.htm#SEC396 63138 3849 3855 stdlocus sing_939.htm#SEC1015 25619 3850 stopTask sing_103 6.htm#SEC111268013851 storeActionOnOrbitConeIndices storeActionOnOrbitConeIndices sing_243 3.htm#SEC2509644283852 stratify sing_1 699.htm#SEC1775567443853 stratify.lib sing_169 7.htm#SEC17733854 stratify_lib sing_169 7.htm#SEC17733856 stopTask sing_1038.htm#SEC1114 6801 3857 storeActionOnOrbitConeIndices storeActionOnOrbitConeIndices sing_2439.htm#SEC2515 64428 3858 stratify sing_1701.htm#SEC1777 56744 3859 stratify.lib sing_1699.htm#SEC1775 3860 stratify_lib sing_1699.htm#SEC1775 3855 3861 string Miscellaneous oddities sing_171.htm#SEC211 3856 3862 string sing_418.htm#IDX297 … … 3860 3866 string related functions string related functions sing_176.htm#SEC216 3861 3867 string type cast sing_174.htm#SEC214 3862 stripHNE sing_1571.htm#SEC1647 19265 3863 sturm sing_2002.htm#SEC2078 54353 3864 sturmha sing_2004.htm#SEC2080 12467 3865 sturmhaseq sing_2005.htm#SEC2081 59133 3866 sturmquery sing_1980.htm#SEC2056 10805 3867 sturmseq sing_2003.htm#SEC2079 23005 3868 submat sing_1056.htm#SEC1132 37665 3869 subquotient sing_2506.htm#SEC2582 40364 3870 subrInterred sing_980.htm#SEC1056 10165 3871 subset_sum01 sing_1923.htm#SEC1999 60620 3872 subset_sum02 sing_1924.htm#SEC2000 37340 3868 stripHNE sing_1573.htm#SEC1649 19265 3869 sturm sing_2004.htm#SEC2080 54353 3870 sturmha sing_2006.htm#SEC2082 12467 3871 sturmhaseq sing_2007.htm#SEC2083 59133 3872 sturmquery sing_1982.htm#SEC2058 10805 3873 sturmseq sing_2005.htm#SEC2081 23005 3874 sublists sing_2344.htm#SEC2420 2979 3875 submat sing_1058.htm#SEC1134 37665 3876 subquotient sing_2513.htm#SEC2589 40364 3877 subrInterred sing_982.htm#SEC1058 10165 3878 subset_sum01 sing_1925.htm#SEC2001 60620 3879 subset_sum02 sing_1926.htm#SEC2002 37340 3873 3880 subst sing_357.htm#SEC397 3874 3881 subst (plural) sing_481.htm#SEC521 3875 substitute sing_9 79.htm#SEC1055289193882 substitute sing_981.htm#SEC1057 28919 3876 3883 sugarCrit, option sing_315.htm#IDX169 3877 3884 sum sing_917.htm#SEC993 555 3878 sum_of_powers sing_226 1.htm#SEC2337121703879 sumlist sing_141 3.htm#SEC1489599183880 sumofquotients sing_27 27.htm#SEC280345693885 sum_of_powers sing_2263.htm#SEC2339 12170 3886 sumlist sing_1415.htm#SEC1491 59918 3887 sumofquotients sing_2734.htm#SEC2810 4569 3881 3888 super-commutative algebras Graded commutative algebras (SCA) sing_490.htm#SEC542 3882 3889 superCommutative sing_734.htm#SEC786 45528 3883 super_increasing_knapsack super_increasing_knapsack sing_193 5.htm#SEC201191773884 surf.lib sing_178 2.htm#SEC18583885 surf_lib sing_178 2.htm#SEC18583886 surfacesignature.lib surfacesignature_lib sing_163 1.htm#SEC17073887 surfacesignature_lib surfacesignature_lib sing_163 1.htm#SEC17073890 super_increasing_knapsack super_increasing_knapsack sing_1937.htm#SEC2013 9177 3891 surf.lib sing_1784.htm#SEC1860 3892 surf_lib sing_1784.htm#SEC1860 3893 surfacesignature.lib surfacesignature_lib sing_1633.htm#SEC1709 3894 surfacesignature_lib surfacesignature_lib sing_1633.htm#SEC1709 3888 3895 surfer sing_1.htm#IDX8 14287 3889 surfer sing_178 4.htm#SEC18603896 surfer sing_1786.htm#SEC1862 3890 3897 surfex sing_1.htm#IDX7 3891 surfex.lib sing_178 5.htm#SEC18613892 surfex_lib sing_178 5.htm#SEC18613898 surfex.lib sing_1787.htm#SEC1863 3899 surfex_lib sing_1787.htm#SEC1863 3893 3900 suspend sing_353.htm#SEC393 3894 swalk sing_27 35.htm#SEC2811167943895 swalk.lib sing_27 34.htm#SEC28103896 swalk_lib sing_27 34.htm#SEC28103897 swap sing_150 0.htm#SEC1576154083898 swap sing_21 79.htm#IDX8453901 swalk sing_2742.htm#SEC2818 16794 3902 swalk.lib sing_2741.htm#SEC2817 3903 swalk_lib sing_2741.htm#SEC2817 3904 swap sing_1502.htm#SEC1578 15408 3905 swap sing_2181.htm#IDX838 3899 3906 switch No case or switch statement sing_412.htm#SEC452 3900 switchRingsAndComputeInitialIdeal switchRingsAndComputeInitialIdeal sing_27 43.htm#SEC281918273901 syModStd sing_134 5.htm#SEC1421502463902 symNsym sing_225 5.htm#SEC2331552303903 sym_gauss sing_108 2.htm#SEC115851213904 symm sing_225 4.htm#SEC2330646283905 symmStd sing_134 4.htm#SEC1420393533906 symmat sing_105 7.htm#SEC1133612943907 symmetric basis sing_107 4.htm#IDX5133908 symmetric power sing_107 6.htm#IDX5153909 symmetricBasis sing_107 4.htm#SEC1150sprintf3910 symmetricPower sing_107 6.htm#SEC115265423911 symmetricPowerSheaf sing_27 13.htm#SEC2789569223912 symmetries sing_224 4.htm#IDX9433913 symmfunc sing_19 89.htm#SEC2065455753914 symodstd.lib sing_13 39.htm#SEC14153915 symodstd_lib sing_13 39.htm#SEC14153916 symsignature sing_19 79.htm#SEC2055105203917 syndrome sing_181 2.htm#SEC1888140573918 sysBin sing_181 0.htm#SEC1886419483919 sysCRHT sing_180 7.htm#SEC1883589303920 sysCRHTMindist sing_18 08.htm#SEC1884136923921 sysFL sing_182 3.htm#SEC1899530403922 sysNewton sing_18 09.htm#SEC1885197043923 sysQE sing_181 3.htm#SEC1889610263924 sys_code sing_180 4.htm#SEC1880202203907 switchRingsAndComputeInitialIdeal switchRingsAndComputeInitialIdeal sing_2750.htm#SEC2826 1827 3908 syModStd sing_1347.htm#SEC1423 50246 3909 symNsym sing_2257.htm#SEC2333 55230 3910 sym_gauss sing_1084.htm#SEC1160 5121 3911 symm sing_2256.htm#SEC2332 64628 3912 symmStd sing_1346.htm#SEC1422 39353 3913 symmat sing_1059.htm#SEC1135 61294 3914 symmetric basis sing_1076.htm#IDX506 3915 symmetric power sing_1078.htm#IDX508 3916 symmetricBasis sing_1076.htm#SEC1152 sprintf 3917 symmetricPower sing_1078.htm#SEC1154 6542 3918 symmetricPowerSheaf sing_2720.htm#SEC2796 56922 3919 symmetries sing_2246.htm#IDX936 3920 symmfunc sing_1991.htm#SEC2067 45575 3921 symodstd.lib sing_1341.htm#SEC1417 3922 symodstd_lib sing_1341.htm#SEC1417 3923 symsignature sing_1981.htm#SEC2057 10520 3924 syndrome sing_1814.htm#SEC1890 14057 3925 sysBin sing_1812.htm#SEC1888 41948 3926 sysCRHT sing_1809.htm#SEC1885 58930 3927 sysCRHTMindist sing_1810.htm#SEC1886 13692 3928 sysFL sing_1825.htm#SEC1901 53040 3929 sysNewton sing_1811.htm#SEC1887 19704 3930 sysQE sing_1815.htm#SEC1891 61026 3931 sys_code sing_1806.htm#SEC1882 20220 3925 3932 system sing_358.htm#SEC398 3926 3933 system, -- sing_358.htm#IDX277 … … 3983 3990 system, version sing_358.htm#IDX273 3984 3991 system, with sing_358.htm#IDX274 3985 systemOfParametersOfLocalization systemOfParametersOfLocalization sing_241 0.htm#SEC2486630943992 systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2416.htm#SEC2492 63094 3986 3993 syz sing_359.htm#SEC399 3987 3994 syz (plural) sing_482.htm#SEC522 3988 tDetropicalise sing_215 7.htm#SEC2233235323989 tInitialForm sing_214 1.htm#SEC2217244843990 tInitialFormPar sing_215 3.htm#SEC222995843991 tInitialFormParMax sing_215 4.htm#SEC223078293992 tInitialIdeal sing_214 2.htm#SEC2218179373993 tab sing_95 2.htm#SEC1028604073994 tail sing_19 58.htm#SEC2034130663995 tame polynomial sing_155 3.htm#IDX7393996 tame polynomial sing_155 4.htm#IDX7493997 tame polynomial sing_155 5.htm#IDX7503998 tangentGens sing_13 69.htm#SEC1445377973999 tangentcone sing_16 18.htm#SEC1694200564000 target sing_25 13.htm#SEC2589187434001 task sing_10 29.htm#IDX5124002 tasks.lib sing_10 29.htm#SEC11054003 tasks_lib sing_10 29.htm#SEC11054004 tau_es sing_152 6.htm#SEC1602170434005 tau_es2 sing_148 0.htm#SEC1556380834006 tdCf sing_229 0.htm#SEC2366215224007 tdFactor sing_229 2.htm#SEC2368379104008 tdProj sing_229 5.htm#SEC2371384064009 tdTerms sing_229 1.htm#SEC2367301664010 teachstd.lib sing_195 6.htm#SEC20324011 teachstd_lib sing_195 6.htm#SEC20323995 tDetropicalise sing_2159.htm#SEC2235 23532 3996 tInitialForm sing_2143.htm#SEC2219 24484 3997 tInitialFormPar sing_2155.htm#SEC2231 9584 3998 tInitialFormParMax sing_2156.htm#SEC2232 7829 3999 tInitialIdeal sing_2144.htm#SEC2220 17937 4000 tab sing_954.htm#SEC1030 60407 4001 tail sing_1960.htm#SEC2036 13066 4002 tame polynomial sing_1555.htm#IDX732 4003 tame polynomial sing_1556.htm#IDX742 4004 tame polynomial sing_1557.htm#IDX743 4005 tangentGens sing_1371.htm#SEC1447 37797 4006 tangentcone sing_1620.htm#SEC1696 20056 4007 target sing_2520.htm#SEC2596 18743 4008 task sing_1031.htm#IDX505 4009 tasks.lib sing_1031.htm#SEC1107 4010 tasks_lib sing_1031.htm#SEC1107 4011 tau_es sing_1528.htm#SEC1604 17043 4012 tau_es2 sing_1482.htm#SEC1558 38083 4013 tdCf sing_2292.htm#SEC2368 21522 4014 tdFactor sing_2294.htm#SEC2370 37910 4015 tdProj sing_2297.htm#SEC2373 38406 4016 tdTerms sing_2293.htm#SEC2369 30166 4017 teachstd.lib sing_1958.htm#SEC2034 4018 teachstd_lib sing_1958.htm#SEC2034 4012 4019 template.lib sing_55.htm#IDX120 4013 4020 template.lib sing_55.htm#IDX123 … … 4015 4022 template_lib sing_55.htm#IDX121 4016 4023 tensor sing_498.htm#IDX311 65451 4017 tensor sing_10 58.htm#SEC11344018 tensorFreeModule sing_25 25.htm#SEC2601593144019 tensorFreemodMod sing_25 24.htm#SEC2600sprintf4020 tensorMatrix sing_252 1.htm#SEC2597314374021 tensorMod sing_117 7.htm#SEC1253219614022 tensorModFreemod sing_25 23.htm#SEC2599118524023 tensorModule sing_252 2.htm#SEC2598587724024 tensorProduct sing_25 26.htm#SEC2602sprintf4025 tensorSheaf sing_271 2.htm#SEC2788240724024 tensor sing_1060.htm#SEC1136 4025 tensorFreeModule sing_2532.htm#SEC2608 59314 4026 tensorFreemodMod sing_2531.htm#SEC2607 sprintf 4027 tensorMatrix sing_2528.htm#SEC2604 31437 4028 tensorMod sing_1179.htm#SEC1255 21961 4029 tensorModFreemod sing_2530.htm#SEC2606 11852 4030 tensorModule sing_2529.htm#SEC2605 58772 4031 tensorProduct sing_2533.htm#SEC2609 sprintf 4032 tensorSheaf sing_2719.htm#SEC2795 24072 4026 4033 term orderings General definitions for orderings sing_859.htm#SEC911 4027 4034 term orderings introduction Introduction to orderings sing_858.htm#SEC910 4028 testFraction sing_265 1.htm#SEC2727284664029 testLocData sing_26 48.htm#SEC2724509864035 testFraction sing_2658.htm#SEC2734 28466 4036 testLocData sing_2655.htm#SEC2731 50986 4030 4037 testNCfac sing_708.htm#SEC760 60394 4031 testNcfrac sing_26 09.htm#SEC2685341864032 testNcfracExamples sing_261 0.htm#SEC2686153994033 testNcloc sing_26 13.htm#SEC2689627064034 testNclocExamples sing_26 14.htm#SEC2690145844035 testOlga sing_26 65.htm#SEC2741539534036 testOlgaExamples sing_26 66.htm#SEC2742628694037 testParametrization sing_138 4.htm#SEC1460186864038 testPointConic sing_138 5.htm#SEC1461253154039 testPrimary sing_129 7.htm#SEC1373342544040 testPrimaryE sing_1 298.htm#SEC1374206934041 tex sing_177 1.htm#SEC1847122264042 texDrawBasic sing_21 48.htm#SEC222436354043 texDrawNewtonSubdivision texDrawNewtonSubdivision sing_215 0.htm#SEC2226420214044 texDrawTriangulation texDrawTriangulation sing_215 1.htm#SEC2227188654045 texDrawTropical sing_21 49.htm#SEC2225584474046 texMatrix sing_214 7.htm#SEC222313344047 texNumber sing_214 5.htm#SEC2221126284048 texPolynomial sing_214 6.htm#SEC2222411364049 texcoef sing_185 2.htm#SEC1928281894050 texdemo sing_177 2.htm#SEC1848130084051 texfactorize sing_177 3.htm#SEC184966824052 texmap sing_177 4.htm#SEC1850352654053 texname sing_177 5.htm#SEC185110084054 texobj sing_177 6.htm#SEC185221074055 texpoly sing_177 7.htm#SEC1853641094056 texproc sing_17 78.htm#SEC1854236264057 texring sing_17 79.htm#SEC1855382754058 the first alternative algorithm sing_115 4.htm#IDX5494059 three_elements sing_194 2.htm#SEC20185134038 testNcfrac sing_2616.htm#SEC2692 34186 4039 testNcfracExamples sing_2617.htm#SEC2693 15399 4040 testNcloc sing_2620.htm#SEC2696 62706 4041 testNclocExamples sing_2621.htm#SEC2697 14584 4042 testOlga sing_2672.htm#SEC2748 53953 4043 testOlgaExamples sing_2673.htm#SEC2749 62869 4044 testParametrization sing_1386.htm#SEC1462 18686 4045 testPointConic sing_1387.htm#SEC1463 25315 4046 testPrimary sing_1299.htm#SEC1375 34254 4047 testPrimaryE sing_1300.htm#SEC1376 20693 4048 tex sing_1773.htm#SEC1849 12226 4049 texDrawBasic sing_2150.htm#SEC2226 3635 4050 texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2152.htm#SEC2228 42021 4051 texDrawTriangulation texDrawTriangulation sing_2153.htm#SEC2229 18865 4052 texDrawTropical sing_2151.htm#SEC2227 58447 4053 texMatrix sing_2149.htm#SEC2225 1334 4054 texNumber sing_2147.htm#SEC2223 12628 4055 texPolynomial sing_2148.htm#SEC2224 41136 4056 texcoef sing_1854.htm#SEC1930 28189 4057 texdemo sing_1774.htm#SEC1850 13008 4058 texfactorize sing_1775.htm#SEC1851 6682 4059 texmap sing_1776.htm#SEC1852 35265 4060 texname sing_1777.htm#SEC1853 1008 4061 texobj sing_1778.htm#SEC1854 2107 4062 texpoly sing_1779.htm#SEC1855 64109 4063 texproc sing_1780.htm#SEC1856 23626 4064 texring sing_1781.htm#SEC1857 38275 4065 the first alternative algorithm sing_1156.htm#IDX542 4066 three_elements sing_1944.htm#SEC2020 513 4060 4067 timeFactorize sing_921.htm#SEC997 49531 4061 4068 timeStd sing_920.htm#SEC996 31506 4062 4069 timer sing_402.htm#SEC442 4063 4070 timer resolution, setting the sing_358.htm#IDX283 4064 timestep sing_239 0.htm#SEC2466382254065 tjurina sing_161 4.htm#SEC169091004066 tmatrix sing_154 1.htm#SEC1617573324067 todd sing_228 7.htm#SEC2363256184068 toddE sing_22 88.htm#SEC2364178234069 toddPoly sing_230 1.htm#SEC2377650664070 tolessvars sing_171 7.htm#SEC1793565904071 topChernClass sing_27 09.htm#SEC2785173744072 topological invariants sing_14 68.htm#IDX6414073 topological invariants sing_147 5.htm#IDX6484074 topological invariants sing_147 6.htm#IDX6524075 topological invariants sing_147 7.htm#IDX6564076 topological invariants sing_14 78.htm#IDX6604071 timestep sing_2396.htm#SEC2472 38225 4072 tjurina sing_1616.htm#SEC1692 9100 4073 tmatrix sing_1543.htm#SEC1619 57332 4074 todd sing_2289.htm#SEC2365 25618 4075 toddE sing_2290.htm#SEC2366 17823 4076 toddPoly sing_2303.htm#SEC2379 65066 4077 tolessvars sing_1719.htm#SEC1795 56590 4078 topChernClass sing_2716.htm#SEC2792 17374 4079 topological invariants sing_1470.htm#IDX634 4080 topological invariants sing_1477.htm#IDX641 4081 topological invariants sing_1478.htm#IDX645 4082 topological invariants sing_1479.htm#IDX649 4083 topological invariants sing_1480.htm#IDX653 4077 4084 toric ideals sing_874.htm#SEC931 4078 toric ring sing_125 6.htm#IDX5824079 toric.lib sing_134 6.htm#SEC14224080 toric_ideal sing_134 7.htm#SEC142357604081 toric_lib sing_134 6.htm#SEC14224082 toric_std sing_13 48.htm#SEC1424261414083 torusInvariants sing_126 2.htm#SEC13389114085 toric ring sing_1258.htm#IDX575 4086 toric.lib sing_1348.htm#SEC1424 4087 toric_ideal sing_1349.htm#SEC1425 5760 4088 toric_lib sing_1348.htm#SEC1424 4089 toric_std sing_1350.htm#SEC1426 26141 4090 torusInvariants sing_1264.htm#SEC1340 911 4084 4091 total divisors sing_498.htm#IDX308 4085 total multiplicities sing_14 68.htm#IDX6444086 totalChernClass sing_27 07.htm#SEC278361534087 totalSegreClass sing_271 0.htm#SEC278632914088 totalmultiplicities sing_147 0.htm#SEC1546582644092 total multiplicities sing_1470.htm#IDX637 4093 totalChernClass sing_2714.htm#SEC2790 6153 4094 totalSegreClass sing_2717.htm#SEC2793 3291 4095 totalmultiplicities sing_1472.htm#SEC1548 58264 4089 4096 trace sing_360.htm#SEC400 4090 tracemult sing_198 3.htm#SEC2059583034097 tracemult sing_1985.htm#SEC2061 58303 4091 4098 transpose sing_361.htm#SEC401 4092 trapezoid sing_23 84.htm#SEC2460615254093 triMNewton sing_174 3.htm#SEC1819628224094 triagmatrix sing_99 3.htm#SEC1069179444095 triang.lib sing_173 6.htm#SEC18124096 triangL sing_173 7.htm#SEC1813518474097 triangL_solve sing_173 4.htm#SEC1810101014098 triangLf_solve sing_173 2.htm#SEC1808497964099 triangLfak sing_17 38.htm#SEC1814500934100 triangM sing_17 39.htm#SEC1815593344101 triangMH sing_174 0.htm#SEC1816342774102 triangM_solve sing_173 3.htm#SEC1809636524103 triang_lib sing_173 6.htm#SEC18124104 triang_solve sing_173 5.htm#SEC1811644044105 triangulations sing_207 3.htm#SEC2149618884106 tropical curves sing_212 7.htm#IDX8224107 tropical geometry sing_114 0.htm#IDX5234108 tropical geometry sing_27 37.htm#IDX10704109 tropical mirror symmetry sing_114 0.htm#IDX5254110 tropical polynomials sing_212 7.htm#IDX8234111 tropical varieties sing_27 37.htm#IDX10714112 tropical.lib sing_212 7.htm#IDX8204113 tropicalCurve sing_213 2.htm#SEC2208168654114 tropicalJInvariant sing_213 5.htm#SEC2211403954115 tropicalLifting sing_21 28.htm#SEC220470524116 tropicalLinkNewton sing_27 45.htm#SEC2821638864117 tropicalNewton.lib sing_27 37.htm#SEC28134118 tropicalNewton_lib sing_27 37.htm#SEC28134119 tropicalPointNewton sing_274 2.htm#SEC2818185724120 tropicalSubst sing_216 0.htm#SEC2236498464121 tropicalVariety sing_216 7.htm#SEC2243390874122 tropicalVarietyNewton tropicalVarietyNewton sing_27 44.htm#SEC2820285324123 tropical_lib sing_212 7.htm#IDX8214124 tropicalise sing_21 39.htm#SEC2215497394125 tropicaliseSet sing_214 0.htm#SEC2216351364126 truncate sing_145 0.htm#SEC1526135454127 truncateFast sing_145 1.htm#SEC152751244128 truncated module sing_145 0.htm#IDX6324129 truncated module sing_145 1.htm#IDX6334099 trapezoid sing_2390.htm#SEC2466 61525 4100 triMNewton sing_1745.htm#SEC1821 62822 4101 triagmatrix sing_995.htm#SEC1071 17944 4102 triang.lib sing_1738.htm#SEC1814 4103 triangL sing_1739.htm#SEC1815 51847 4104 triangL_solve sing_1736.htm#SEC1812 10101 4105 triangLf_solve sing_1734.htm#SEC1810 49796 4106 triangLfak sing_1740.htm#SEC1816 50093 4107 triangM sing_1741.htm#SEC1817 59334 4108 triangMH sing_1742.htm#SEC1818 34277 4109 triangM_solve sing_1735.htm#SEC1811 63652 4110 triang_lib sing_1738.htm#SEC1814 4111 triang_solve sing_1737.htm#SEC1813 64404 4112 triangulations sing_2075.htm#SEC2151 61888 4113 tropical curves sing_2129.htm#IDX815 4114 tropical geometry sing_1142.htm#IDX516 4115 tropical geometry sing_2744.htm#IDX1068 4116 tropical mirror symmetry sing_1142.htm#IDX518 4117 tropical polynomials sing_2129.htm#IDX816 4118 tropical varieties sing_2744.htm#IDX1069 4119 tropical.lib sing_2129.htm#IDX813 4120 tropicalCurve sing_2134.htm#SEC2210 16865 4121 tropicalJInvariant sing_2137.htm#SEC2213 40395 4122 tropicalLifting sing_2130.htm#SEC2206 7052 4123 tropicalLinkNewton sing_2752.htm#SEC2828 63886 4124 tropicalNewton.lib sing_2744.htm#SEC2820 4125 tropicalNewton_lib sing_2744.htm#SEC2820 4126 tropicalPointNewton sing_2749.htm#SEC2825 18572 4127 tropicalSubst sing_2162.htm#SEC2238 49846 4128 tropicalVariety sing_2169.htm#SEC2245 39087 4129 tropicalVarietyNewton tropicalVarietyNewton sing_2751.htm#SEC2827 28532 4130 tropical_lib sing_2129.htm#IDX814 4131 tropicalise sing_2141.htm#SEC2217 49739 4132 tropicaliseSet sing_2142.htm#SEC2218 35136 4133 truncate sing_1452.htm#SEC1528 13545 4134 truncateFast sing_1453.htm#SEC1529 5124 4135 truncated module sing_1452.htm#IDX625 4136 truncated module sing_1453.htm#IDX626 4130 4137 tst_ncfactor sing_716.htm#SEC768 3339 4131 twalk sing_115 3.htm#SEC1229357534138 twalk sing_1155.htm#SEC1231 35753 4132 4139 two-sided sing_498.htm#IDX309 4133 4140 two-sided Groebner basis sing_498.htm#IDX310 … … 4135 4142 twostd sing_483.htm#SEC523 4136 4143 type sing_362.htm#SEC402 4137 type B sing_219 5.htm#IDX8724138 type D sing_219 6.htm#IDX8744144 type B sing_2197.htm#IDX865 4145 type D sing_2198.htm#IDX867 4139 4146 type,custom Definition of a user defined type sing_183.htm#SEC223 4140 type2arr sing_217 3.htm#SEC2249626244141 typecasting sing_217 3.htm#IDX8284142 typecasting sing_217 4.htm#IDX8304143 typecasting sing_217 5.htm#IDX8334147 type2arr sing_2175.htm#SEC2251 62624 4148 typecasting sing_2175.htm#IDX821 4149 typecasting sing_2176.htm#IDX823 4150 typecasting sing_2177.htm#IDX826 4144 4151 typeof sing_363.htm#SEC403 4145 u sing_23 76.htm#SEC2452121544152 u sing_2382.htm#SEC2458 12154 4146 4153 uname sing_358.htm#IDX269 4147 unbounded_knapsack sing_192 5.htm#SEC2001172264148 unipotent groups sing_13 68.htm#IDX6004149 uniquePoint sing_205 2.htm#SEC21288934150 unitMatrix sing_26 79.htm#SEC2755330144151 unitmat sing_10 59.htm#SEC1135128624154 unbounded_knapsack sing_1927.htm#SEC2003 17226 4155 unipotent groups sing_1370.htm#IDX593 4156 uniquePoint sing_2054.htm#SEC2130 893 4157 unitMatrix sing_2686.htm#SEC2762 33014 4158 unitmat sing_1061.htm#SEC1137 12862 4152 4159 univariate sing_364.htm#SEC404 4153 univarpoly sing_199 0.htm#SEC2066462884160 univarpoly sing_1992.htm#SEC2068 46288 4154 4161 unknown syndrome Decoding method based on quadratic equations sing_890.htm#SEC961 4155 4162 unset sing_276.htm#SEC316 4156 4163 untyped definitions sing_88.htm#SEC128 4157 4164 untyped definitions sing_423.htm#SEC463 4158 updatePairs sing_19 68.htm#SEC2044511444159 ures_solve sing_172 6.htm#SEC1802324494165 updatePairs sing_1970.htm#SEC2046 51144 4166 ures_solve sing_1728.htm#SEC1804 32449 4160 4167 uressolve sing_365.htm#SEC405 4161 4168 usage, option sing_315.htm#IDX185 4162 4169 user interface, Emacs Emacs user interface sing_21.htm#SEC28 4163 vStd sing_233 4.htm#SEC2410123214164 val sing_27 39.htm#SEC2815621714165 valvars sing_172 1.htm#SEC1797157234170 vStd sing_2336.htm#SEC2412 12321 4171 val sing_2746.htm#SEC2822 62171 4172 valvars sing_1723.htm#SEC1799 15723 4166 4173 vandermonde sing_366.htm#SEC406 4167 vanishId sing_182 2.htm#SEC1898491484174 vanishId sing_1824.htm#SEC1900 49148 4168 4175 var sing_367.htm#SEC407 4169 varMat sing_217 7.htm#SEC2253517724170 varNum sing_21 78.htm#SEC2254184854176 varMat sing_2179.htm#SEC2255 51772 4177 varNum sing_2180.htm#SEC2256 18485 4171 4178 variables sing_368.htm#SEC408 4172 variables sing_217 7.htm#IDX8404173 variables sing_21 78.htm#IDX8424174 variables sing_21 79.htm#IDX8464175 variables sing_218 0.htm#IDX8484179 variables sing_2179.htm#IDX833 4180 variables sing_2180.htm#IDX835 4181 variables sing_2181.htm#IDX839 4182 variables sing_2182.htm#IDX841 4176 4183 variablesSorted sing_536.htm#SEC588 13533 4177 4184 variablesStandard sing_535.htm#SEC587 56500 4178 4185 vars2pars sing_795.htm#SEC847 47343 4179 varsigns sing_199 5.htm#SEC207134714186 varsigns sing_1997.htm#SEC2073 3471 4180 4187 varstr sing_369.htm#SEC409 4181 4188 vct2str sing_657.htm#SEC709 51983 … … 4188 4195 vector operations sing_180.htm#SEC220 4189 4196 vector related functions vector related functions sing_181.htm#SEC221 4190 verify sing_198 6.htm#SEC2062322714191 versal sing_152 1.htm#SEC1597462474197 verify sing_1988.htm#SEC2064 32271 4198 versal sing_1523.htm#SEC1599 46247 4192 4199 version sing_358.htm#IDX272 4193 vertexAdjacencyGraph vertexAdjacencyGraph sing_212 0.htm#SEC2196601024194 vertexEdgeGraph sing_212 1.htm#SEC2197328164195 vertices sing_20 68.htm#SEC2144113984196 vfilt sing_15 39.htm#SEC161592834197 view sing_184 2.htm#SEC1918292844198 visual sing_212 2.htm#SEC2198514344199 visualize sing_23 75.htm#SEC245167504200 vertexAdjacencyGraph vertexAdjacencyGraph sing_2122.htm#SEC2198 60102 4201 vertexEdgeGraph sing_2123.htm#SEC2199 32816 4202 vertices sing_2070.htm#SEC2146 11398 4203 vfilt sing_1541.htm#SEC1617 9283 4204 view sing_1844.htm#SEC1920 29284 4205 visual sing_2124.htm#SEC2200 51434 4206 visualize sing_2381.htm#SEC2457 6750 4200 4207 voice sing_405.htm#SEC445 4201 vwfilt sing_154 0.htm#SEC161682814202 wUnit sing_188 0.htm#SEC1956271984203 waitAllTasks sing_10 38.htm#SEC111470874204 waitTasks sing_103 7.htm#SEC1113528574208 vwfilt sing_1542.htm#SEC1618 8281 4209 wUnit sing_1882.htm#SEC1958 27198 4210 waitAllTasks sing_1040.htm#SEC1116 7087 4211 waitTasks sing_1039.htm#SEC1115 52857 4205 4212 waitall sing_371.htm#SEC411 4206 4213 waitfirst sing_372.htm#SEC412 4207 walk, groebner sing_115 1.htm#IDX5454208 walk, groebner sing_25 37.htm#IDX9934209 walk, groebner sing_269 1.htm#IDX10394210 walk, groebner sing_27 34.htm#IDX10684211 warkedPreimageStd sing_241 2.htm#SEC2488147594214 walk, groebner sing_1153.htm#IDX538 4215 walk, groebner sing_2544.htm#IDX991 4216 walk, groebner sing_2698.htm#IDX1037 4217 walk, groebner sing_2741.htm#IDX1066 4218 warkedPreimageStd sing_2418.htm#SEC2494 14759 4212 4219 warn, option sing_70.htm#SEC110 4213 4220 warn, option sing_315.htm#IDX151 4214 4221 watchdog sing_918.htm#SEC994 sprintf 4215 4222 wedge sing_373.htm#SEC413 4216 weierstr.lib sing_197 1.htm#SEC20474217 weierstrDiv sing_197 2.htm#SEC20482604218 weierstrPrep sing_197 3.htm#SEC204957524219 weierstr_lib sing_197 1.htm#SEC20474220 weierstrassForm sing_213 6.htm#SEC2212608744223 weierstr.lib sing_1973.htm#SEC2049 4224 weierstrDiv sing_1974.htm#SEC2050 260 4225 weierstrPrep sing_1975.htm#SEC2051 5752 4226 weierstr_lib sing_1973.htm#SEC2049 4227 weierstrassForm sing_2138.htm#SEC2214 60874 4221 4228 weight sing_374.htm#SEC414 4222 weight filtration sing_153 1.htm#IDX6724223 weight filtration sing_15 38.htm#IDX7064224 weight filtration sing_154 0.htm#IDX7204225 weight filtration sing_154 1.htm#IDX7284226 weight filtration sing_155 3.htm#IDX7444227 weight filtration sing_155 5.htm#IDX7554229 weight filtration sing_1533.htm#IDX665 4230 weight filtration sing_1540.htm#IDX699 4231 weight filtration sing_1542.htm#IDX713 4232 weight filtration sing_1543.htm#IDX721 4233 weight filtration sing_1555.htm#IDX737 4234 weight filtration sing_1557.htm#IDX748 4228 4235 weightKB sing_375.htm#SEC415 21753 4229 4236 weightM, option sing_315.htm#IDX170 … … 4231 4238 weighted reverse lexicographical ordering Global orderings sing_860.htm#IDX397 4232 4239 weightedRing sing_727.htm#SEC779 33786 4233 whichvariable sing_199 4.htm#SEC2070271224240 whichvariable sing_1996.htm#SEC2072 27122 4234 4241 while sing_392.htm#SEC432 4235 4242 withDim sing_209.htm#IDX145 … … 4240 4247 wp, global ordering sing_860.htm#IDX398 4241 4248 write sing_376.htm#SEC416 4242 writeNmzData sing_127 3.htm#SEC1349384674243 writeNmzPaths sing_127 7.htm#SEC1353sprintf4249 writeNmzData sing_1275.htm#SEC1351 38467 4250 writeNmzPaths sing_1279.htm#SEC1355 sprintf 4244 4251 ws, local ordering sing_861.htm#IDX409 4245 wurzel sing_186 2.htm#SEC1938127554246 xchange sing_185 6.htm#SEC1932407414247 xdvi sing_178 1.htm#SEC1857168984248 zdd sing_222 4.htm#IDX9214249 zdd2poly sing_224 1.htm#SEC2317550474250 zero sing_24 86.htm#SEC2562120604251 zero-dimensional sing_199 1.htm#IDX8114252 zeroMod sing_121 3.htm#SEC1289606094253 zeroNcfrac sing_260 2.htm#SEC2678508404254 zeroOpt sing_122 2.htm#SEC1298192604255 zeroRadical sing_112 2.htm#SEC1198355984256 zeroSet sing_17 49.htm#SEC1825600304257 zerodec sing_130 6.htm#SEC1382307654258 zeroset.lib sing_174 4.htm#SEC18204259 zeroset_lib sing_174 4.htm#SEC18204260 zetaDL sing_144 3.htm#SEC1519sprintf4252 wurzel sing_1864.htm#SEC1940 12755 4253 xchange sing_1858.htm#SEC1934 40741 4254 xdvi sing_1783.htm#SEC1859 16898 4255 zdd sing_2226.htm#IDX914 4256 zdd2poly sing_2243.htm#SEC2319 55047 4257 zero sing_2493.htm#SEC2569 12060 4258 zero-dimensional sing_1993.htm#IDX804 4259 zeroMod sing_1215.htm#SEC1291 60609 4260 zeroNcfrac sing_2609.htm#SEC2685 50840 4261 zeroOpt sing_1224.htm#SEC1300 19260 4262 zeroRadical sing_1124.htm#SEC1200 35598 4263 zeroSet sing_1751.htm#SEC1827 60030 4264 zerodec sing_1308.htm#SEC1384 30765 4265 zeroset.lib sing_1746.htm#SEC1822 4266 zeroset_lib sing_1746.htm#SEC1822 4267 zetaDL sing_1445.htm#SEC1521 sprintf 4261 4268 { sing_36.htm#IDX78 4262 4269 || sing_36.htm#IDX103 -
emacs/hlp-cmpl.el
r0e896f r315439 100 100 ("addvarsTo" . "addvarsTo. (line 6") 101 101 ("ademRelations" . "ademRelations. (line 6") 102 ("ADGT" . "ADGT. (line 6") 102 103 ("Adj_div" . "Adj_div. (line 6") 103 104 ("adjoint" . "adjoint. (line 6") 104 ("Adjoint ideal" . "paraplanecurves_lib. (line 7 3")105 ("Adjoint ideal" . "paraplanecurves_lib. (line 78") 105 106 ("adjointIdeal" . "adjointIdeal. (line 6") 106 107 ("adjunction divisor" . "Adj_div. (line 64") … … 242 243 ("autgradalg.lib" . "autgradalg_lib. (line 6") 243 244 ("autgradalg_lib" . "autgradalg_lib. (line 6") 244 ("Authors" . "Preface. (line 14 4")245 ("Authors" . "Preface. (line 145") 245 246 ("autKS" . "autKS. (line 6") 246 ("Automatic Deduction of Geometric Theorems" . "grobcov_lib. (line 135") 247 ("Automatic Deduction" . "ADGT. (line 51") 248 ("Automatic Demonstration" . "ADGT. (line 51") 247 249 ("automorphism group" . "autgradalg_lib. (line 61") 248 250 ("automorphisms" . "autgradalg_lib. (line 61") … … 377 379 ("cancelunit, option" . "option. (line 145") 378 380 ("canoncial form" . "PtoCrep. (line 23") 379 ("canonical" . " extendGC. (line 49")380 ("canonical form" . " ConsLevelsToLevels.(line 25")381 (" Canonical Forms" . "grobcov_lib. (line 135")381 ("canonical" . "grobcov. (line 121") 382 ("canonical form" . "Levels. (line 25") 383 ("canonical," . "extendGC. (line 49") 382 384 ("canonicalizeCone" . "canonicalizeCone. (line 6") 383 385 ("canonize" . "canonize. (line 6") … … 489 491 ("cisimplicial.lib" . "cisimplicial_lib. (line 6") 490 492 ("cisimplicial_lib" . "cisimplicial_lib. (line 6") 491 ("classification" . "classify2_lib. (line 50")493 ("classification" . "classify2_lib. (line 60") 492 494 ("Classification of hypersurface singularities" . "Classification of hypersurface singularities") 493 495 ("Classification of singularities" . "realclassify. (line 43") … … 542 544 ("colrank" . "colrank. (line 6") 543 545 ("colred" . "colred. (line 6") 546 ("combinat.lib" . "combinat_lib. (line 6") 547 ("combinat_lib" . "combinat_lib. (line 6") 544 548 ("comma" . "Usage of commas. (line 6") 545 549 ("Command line options" . "Command line options") … … 573 577 ("Comprehensive Groebner System" . "cgsdr. (line 96") 574 578 ("comprehensive Groebner system" . "compregb_lib. (line 27") 575 ("Comprehensive Groebner Systems" . "grobcov_lib. (line 135")576 579 ("compress" . "compress. (line 6") 577 580 ("computeAfaceOrbits" . "computeAfaceOrbits. (line 6") … … 592 595 ("conicWithTangents" . "conicWithTangents. (line 6") 593 596 ("ConsLevels" . "ConsLevels. (line 6") 594 ("ConsLevelsToLevels" . "ConsLevelsToLevels. (line 6")595 597 ("constructblwup" . "constructblwup. (line 6") 596 598 ("constructH" . "constructH. (line 6") 597 599 ("constructible set" . "ConsLevels. (line 36") 598 ("constructible sets" . "ConsLevelsToLevels. (line 25") 599 ("Constructible sets" . "grobcov_lib. (line 135") 600 ("constructible sets" . "Levels. (line 25") 600 601 ("constructlastblwup" . "constructlastblwup. (line 6") 601 602 ("constructor" . "multarr2arr. (line 14") … … 617 618 ("contributionBundle" . "contributionBundle. (line 6") 618 619 ("contributors" . "system. (line 53") 619 ("Contributors" . "Preface. (line 14 4")620 ("Contributors" . "Preface. (line 145") 620 621 ("control" . "control. (line 6") 621 622 ("Control structures" . "Control structures. (line 6") … … 679 680 ("CurveParam" . "CurveParam. (line 6") 680 681 ("CurveRes" . "CurveRes. (line 6") 681 ("Curves" . "paraplanecurves_lib. (line 7 3")682 ("Curves" . "paraplanecurves_lib. (line 78") 682 683 ("custom assignment" . "Assignments for user defined types") 683 684 ("custom command" . "Commands for user defined types") … … 711 712 ("dec1var" . "dec1var. (line 6") 712 713 ("decimal" . "decimal. (line 6") 713 ("Decker, Wolfram" . "Preface. (line 14 4")714 ("Decker, Wolfram" . "Preface. (line 145") 714 715 ("Declaration of objects of a user defined type" . "Declaration of objects of a user defined type") 715 716 ("decode" . "decode. (line 6") … … 812 813 ("discrepancy" . "discrepancy. (line 6") 813 814 ("discrim" . "discrim. (line 6") 814 ("discussion of parametric ideal" . " extendGC. (line 49")815 ("discussion of parametric ideal" . "grobcov. (line 121") 815 816 ("disjoint" . "cgsdr. (line 96") 816 817 ("disp_zdd" . "disp_zdd. (line 6") … … 871 872 ("dump" . "dump. (line 6") 872 873 ("dynamic geometry" . "locusdg. (line 21") 873 ("Dynamic Geometry" . "grobcov_lib. (line 135")874 874 ("Dynamic loading" . "Dynamic loading. (line 6") 875 875 ("Dynamic modules" . "Dynamic modules. (line 6") … … 939 939 ("Enumerative geometry" . "schubert_lib. (line 97") 940 940 ("envelop" . "FamElemsAtEnvCompPoints") 941 ("Envelope" . "grobcov_lib. (line 135")942 941 ("envelope" . "envelope. (line 6") 943 942 ("enveloping algebra" . "bimodules_lib. (line 71") … … 1189 1188 ("genSymId" . "genSymId. (line 6") 1190 1189 ("genus" . "genus. (line 6") 1191 ("Geometric genus" . "paraplanecurves_lib. (line 7 3")1190 ("Geometric genus" . "paraplanecurves_lib. (line 78") 1192 1191 ("Geometric Invariant Theory" . "Geometric Invariant Theory") 1192 ("Geometric Theorems" . "ADGT. (line 51") 1193 1193 ("geometrical locus" . "FamElemsAtEnvCompPoints") 1194 1194 ("German Umlaute" . "Limitations. (line 54") … … 1274 1274 ("grconcat" . "grconcat. (line 6") 1275 1275 ("grdeg" . "grdeg. (line 6") 1276 ("Greuel, Gert-Martin" . "Preface. (line 14 4")1276 ("Greuel, Gert-Martin" . "Preface. (line 145") 1277 1277 ("grgens" . "grgens. (line 6") 1278 1278 ("grgroebner" . "grgroebner. (line 6") … … 1295 1295 ("Groebner basis conversion" . "Groebner basis conversion") 1296 1296 ("Groebner cover" . "extendGC. (line 49") 1297 ("Groebner Cover" . "grobcov_lib. (line 135")1298 1297 ("Groebner fan" . "polymake_lib. (line 119") 1299 1298 ("Groebner walk" . "rwalk. (line 22") … … 1538 1537 ("intersectionValRings" . "intersectionValRings") 1539 1538 ("intersectLattices" . "intersectLattices. (line 6") 1539 ("intersectLists" . "intersectLists. (line 6") 1540 1540 ("intersectMon" . "intersectMon. (line 6") 1541 1541 ("intersectOrbitsWithMovingCone" . "intersectOrbitsWithMovingCone") 1542 ("intersectpar" . "intersectpar. (line 6") 1542 1543 ("intersectSyz, option" . "option. (line 158") 1543 1544 ("IntersectWithSub" . "IntersectWithSub. (line 6") … … 1819 1820 ("LETTERPLACE" . "LETTERPLACE. (line 6") 1820 1821 ("letterplace correspondence" . "Letterplace correspondence") 1822 ("Levels" . "Levels. (line 6") 1821 1823 ("lex_solve" . "lex_solve. (line 6") 1822 1824 ("Lexicographic Groebner bases, computation of" . "Groebner basis conversion") … … 1881 1883 ("list operations" . "list operations. (line 6") 1882 1884 ("list related functions" . "list related functions") 1885 ("lists" . "intersectLists. (line 16") 1886 ("lists, elements" . "member. (line 16") 1883 1887 ("listvar" . "listvar. (line 6") 1884 1888 ("lll" . "lll. (line 6") … … 1900 1904 ("localstd" . "localstd. (line 6") 1901 1905 ("locAtZero" . "locAtZero. (line 6") 1902 ("Loci" . "grobcov_lib. (line 135")1903 1906 ("locNormal" . "locNormal. (line 6") 1904 1907 ("locnormal.lib" . "locnormal_lib. (line 6") … … 2059 2062 ("mdouble" . "mdouble. (line 6") 2060 2063 ("mem, option" . "option. (line 193") 2064 ("member" . "member. (line 6") 2061 2065 ("membershipMon" . "membershipMon. (line 6") 2062 2066 ("memory" . "memory. (line 6") … … 2064 2068 ("merkle_hellman_decryption" . "merkle_hellman_decryption") 2065 2069 ("merkle_hellman_encryption" . "merkle_hellman_encryption") 2070 ("methods, hashtables" . "methods_lib. (line 33") 2071 ("methods.lib" . "methods_lib. (line 6") 2072 ("methods_lib" . "methods_lib. (line 6") 2066 2073 ("midpoint" . "midpoint. (line 6") 2067 2074 ("MillerRabin" . "MillerRabin. (line 6") … … 2501 2508 ("parametric annihilator for variety" . "dmodvar_lib. (line 59") 2502 2509 ("parametric ideal" . "extendGC. (line 49") 2503 ("Parametric Polynomial Systems" . "grobcov_lib. (line 135")2504 2510 ("parametrization" . "param. (line 36") 2505 ("Parametrization" . "paraplanecurves_lib. (line 7 3")2511 ("Parametrization" . "paraplanecurves_lib. (line 78") 2506 2512 ("parametrization" . "parametrizeOrbit. (line 34") 2507 2513 ("Parametrization, image." . "testParametrization. (line 26") … … 2535 2541 ("permutationFromIntvec" . "permutationFromIntvec") 2536 2542 ("permutations" . "permute. (line 22") 2543 ("permutations, sum, max, min" . "combinat_lib. (line 18") 2537 2544 ("permutationToIntvec" . "permutationToIntvec. (line 6") 2538 2545 ("permute" . "permute. (line 6") … … 2544 2551 ("PEsolve" . "PEsolve. (line 6") 2545 2552 ("pFactor" . "pFactor. (line 6") 2546 ("Pfister, Gerhard" . "Preface. (line 14 4")2553 ("Pfister, Gerhard" . "Preface. (line 145") 2547 2554 ("PH_ais" . "PH_ais. (line 6") 2548 2555 ("PH_nais" . "PH_nais. (line 6") … … 2614 2621 ("Pottier algorithm" . "Pottier. (line 6") 2615 2622 ("power" . "power. (line 6") 2623 ("power set" . "sublists. (line 15") 2616 2624 ("power_products" . "power_products. (line 6") 2617 2625 ("powerN" . "powerN. (line 6") … … 2826 2834 ("ratgb.lib" . "ratgb_lib. (line 6") 2827 2835 ("ratgb_lib" . "ratgb_lib. (line 6") 2828 ("Rational curves" . "paraplanecurves_lib. (line 7 3")2836 ("Rational curves" . "paraplanecurves_lib. (line 78") 2829 2837 ("rational curves, rational parametrization of rational curves." . "paraPlaneCurve") 2830 2838 ("rational normal curve, projection." . "rncItProjEven. (line 30") … … 3050 3058 ("scalarProd" . "scalarProd. (line 6") 3051 3059 ("scheme" . "scheme. (line 6") 3052 ("Scho\"nemann, Hans" . "Preface. (line 14 4")3060 ("Scho\"nemann, Hans" . "Preface. (line 145") 3053 3061 ("Schoof" . "Schoof. (line 6") 3054 3062 ("Schubert calculus" . "schubert_lib. (line 97") … … 3161 3169 ("Singular2bertini" . "Singular2bertini. (line 6") 3162 3170 ("SINGULARHIST" . "Editing input. (line 6") 3163 ("singularities" . "classify2_lib. (line 50")3171 ("singularities" . "classify2_lib. (line 60") 3164 3172 ("Singularities" . "Singularities. (line 6") 3165 3173 ("singularities, resolution of" . "Resolution of singularities") … … 3295 3303 ("sturmquery" . "sturmquery. (line 6") 3296 3304 ("sturmseq" . "sturmseq. (line 6") 3305 ("sublists" . "sublists. (line 6") 3297 3306 ("submat" . "submat. (line 6") 3298 3307 ("subquotient" . "subquotient. (line 6")
Note: See TracChangeset
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